The Fifteenth Workshop on Numerical Ranges and Numerical Radii (WONRA)

West Gate (Second)

Building 1

June 21-24, 2019 at Toyo University, Kawagoe Campus

Purpose

This is one of the couple of the special workshops for the celebrated Toeplitz-Hausdorff Theorem. The year 2018 was the 100 anniversary of the celebrated Toeplitz-Hausdorff Theorem asserting the numerical range of an operator is always convex. There has been many research activities on the topic after this fundamental result was established. The high level of research activities are due to the many connections of the subject to different pure and applied areas. The purpose of the workshop is to stimulate research and foster interaction of researchers interested in the subject. The informal workshop atmosphere will facilitate the exchange of ideas from different research areas and, hopefully, the participants will leave informed of the latest developments and newest ideas. One may visit the website WONRA to see some background about the subject and previous meetings, and the Wiki page for the history of the workshop and related meetings on the subject. Furthermore, to celebrate the 100 anniversary of the Toplitz- Hausdorff Theorem. Another special workshop was held in Germany in summer of 2018, and the 2020 workshop following the usual schedule will take place in Coimbra in the summer of 2020. Support

This work was supported by JSPS KAKENHI Grant Number JP17K05285 (Hiroyuki Osaka). Organizers

 Chi-Kwong Li, College of William and Mary.  Hiroshi Nakazato, Hirosaki University.  Hiroyuki Osaka, Ritsumeikan University.  Takeaki Yamazaki, Toyo University.

Venue

 Toyo University, Kawagoe Campus, 2nd floor of Building 1. 2100 Kujirai Kawagoe-shi, Saitama, 350-8585, Japan.

21, June: Registration at room 1205. 22~23, June: Registration at room 1205. Talks at 1206.

Registration

 Registration fee is 5000 Yen (students for free).  The conference fee should be paid at registration. Sorry any credit card is not accepted.

2 Access

 From Narita Airport 1) Bus Narita Airport – (Tobu bus)- Kawagoe Station (3,300 yen) Kawagoe Station – (Tobu Tojo line) – Tsurugasima

2) Train Narita Airport – (KEISEI Sky liner) – Nippori – (JR Yamanote line) – Ikebukuro – (Tobu Tojo line) – Tsurugasima

 From Haneda Airport 1) Bus Haneda Airport – (Airport Limousine Bus)- Kawagoe Station (1,750 yen) Kawagoe Station –– (Tobu Tojo line)- Tsurugashima

2) Train Haneda Airport – (Keikyu line) – Shinagawa – (JR Yamanote line) - Ikebukuro – (Tobu Tojo line) – Tsurugasima

 From Tokyo Station 1) Train Tokyo – (JR Yamanote line) – Ikebukuro – (Tobu Tojo line) – Tsurugasima

 From Ikebukuro 1) Train Ikebukuro – (Tobu Tojo line) – Tsurugasima

 From Kawagoe 1) Train Kawagoe – (Tobu Tojo line) – Tsurugasima (10 min.)

The conference place is located in 20 minutes from the ``Tsurugashima station’’ on foot.

Taxi to Toyo University

From Fee Narita Airport 36,000 yen Haneda Airport 21,000 yen Kawagoe Station 2,500 yen Tsurugashima Station 1,000 yen

3 Time Table for Airport Bus

From Narita Airport (get off at Kawagoe Station West Exit)

See more information at http://www.tobu-bus.com/en/narita/narita_kawagoe.html

4 From Haneda Airport (get off at Kawagoe Station West)

See more information at https://www.limousinebus.co.jp/en/areas/detail/hnd/kawagoe/for

Bus stop at Kawagoe station (Narita and Haneda airports).

5 Program

22, June (Sat)

Chair Chi-Kwong Li (College of William and Mary, USA)

Ilya Spitkovsky (New York University Abu Dhabi, UAE) 10:00~10:30 Inverse continutiy of the numerical range map Kennett Dela Rosa (Drexel University, USA) 10:30~11:00 Location of Ritz values in the numerical range of normal matrices

Break

Pan Shun Lau (University of Nevada Reno, USA) 11:15~11:45 The decomposable numerical range of derivations Muneo Cho (Kanagawa University, Japan) 11:45~12:15 Numerical ranges of Banach space operators

Lunch

Chair Nataria Bebiano (University of Coimbra, Portugal)

Hiroshi Nakazato (Hirosaki University, Japan) 14:00~14:30 Period matrix of a Riemann surface and the numerical range Mao-Ting Chien (Soochow University, Taiwan) 14:30~15:00 Computing the diameter and width of the numerical range Masayo Fujimura (National Defense Academy of Japan, Japan) 15:00~15:30 Geometry of finite Blaschke products: pentagons and pentagrams

Break

Chair Mao-Ting Chien (Soochow University, Taiwan)

Patrick Rault (University of Nebraska at Omaha, USA) 16:00~16:30 Singularities of Base Polynomials and Gau-Wu Numbers Michiya Mori (The University of Tokyo, Japan) 16:30~17:00 Order isomorphisms of von Neumann algebras An-Bao Xu (Wenzhou University, China) 17:00~17:30 Parametrized quasi-soft thresholding operator for compressed sensing

6 23 , June (Sun)

Chair Hiroyuki Osaka (Ritsumeikan University, Japan)

Chi-Kwong Li (College of William and Mary, USA) 10:00~10:30 Numerical ranges, operator systems, and quantum channels Natalia Bebiano (University of Coimbra, Portugal) 10:30~11:00 The thermodynamics of systems described by non-Hermitian Hamiltonian

Break

Seung-Hyeok Kye (Seoul National University, Korea) 11:15~11:45 Roles of exposed indecomposable positive multi-linear maps in quantum information theory Ramesh Golla (IIT, India) 11:45~12:15 On a subclass of norm attaining operators

Lunch

Chair Takeaki Yamazaki (Toyo University, Japan)

Yongdo Lim (Sungkyunkwan University, Korea) 14:00~14:30 Polar decompositions and Aluthge transforms Yuki Seo (Osaka Kyoiku University, Japan) 14:30~15:00 Numerical radius inequalities related to the geometric means of negative power Shigeru Furuichi (Nihon University, Japan) 15:00~15:30 Generalization and improvements of numerical radius inequalities

Break

Chair Hiroshi Nakazato (Hirosaki University, Japan)

Jinchuan Hou (Taiyuan University of Technology, China) 16:00~16:30 Preservers of numerical radius on Lie products of self-adjoint operators Ming-Cheng Tsai (Taipei University of Technology, Taiwan) 16:30~17:00 Nonsurjective maps between rectangular matrices preserving disjointness, (zero) triple Shuhei Wada (National Institute of Technology, Kisarazu College, Japan) 17:00~17:30 Ando-Hiai type inequalities for operator means and operator perspectives

Social Events

Registration 21, June, 18:00~20:00 Banquet 23, June 18:30~20:30 Excursion 24, June 10:00~12:00

7 Banquet

Date 23/6/2019 (Sun.) 18:30—20:30 Place Alcazar Geihinkan Kawagoe (アルカーサル迎賓館川越 ) Address 4-11, Shinden Kujirai Kawagoe-Shi, Saitama 350-0809, Japan Phone +81-49-231-7777

Access Map

Excursion

Date 24/6/2019 (Mon.) 9:45—12:10 Nearby the Automatic Ticket Gate of Kawagoe Station, Meeting Place Tobu Tojo Line Schedule Go to Kitain Temple, 500 Stone Statues and Old Storehouse Area

Because we have two guides, we divide into two groups (both guide takes us the same course). Please fill your name in the list of one of the groups which you want to join in.

8 Restaurants 9

University Restaurant (1F) and Shop (2F) open on Saturday 8:30—14:00. Abstract

22, June (Saturday)

• 10:00–10:30 Ilya M. Spitkovsky ([email protected] and [email protected]) Mathematics Program, New York University Abu Dhabi (NYUAD), UAE Title: Inverse continutiy of the numerical range map

Abstract: Let A be a linear bounded operator acting on a Hilbert space H. The numerical range W (A) of A can be thought of as the image of the units sphere of H under the numerical range generating function fA : x 7→ (Ax, x). This talk is devoted to continuity −1 properties of the (multivalued) inverse mapping fA . In particular, strong continuity of −1 fA on the interior of W (A) is established. Co-author: Brian Lins (Hampden-Sydney College, Virginia, USA).

• 10:30–11:00 Paul Reine Kennett L. Dela Rosa ([email protected]) Department of Mathematics, Drexel University, USA Title: Location of Ritz values in the numerical range of normal matrices

Abstract: In 2013, Carden and Hansen proved that ﬁxing µ1 ∈ W (A)\∂W (A), where A ∈ 3×3 C is a normal matrix with noncollinear eigenvalues, determines a unique number µ2 ∈ W (A) so that {µ1, µ2} forms a 2-Ritz set for A. They recognized that µ2 is the isogonal conjugate of µ1 with respect to the triangle formed by connecting the three eigenvalues of A. In this talk, we consider the analogous problem for a 4-by-4 normal matrix A. In particular, given µ1 ∈ W (A) in the interior of one of the quadrants formed by the diagonals of W (A), we prove that if {µ1, µ2} forms a 2-Ritz set, then µ2 lies in the convex hull of two eigenvalues of A and the two isogonal conjugates of µ1 with respect to the two triangles containing µ1. We examine how such a result can be used to understand 2-Ritz sets of n-by-n normal matrices. Co-author(s): Hugo J. Woerdeman (Department of Mathematics, Drexel University, USA).

10 • 11:15–11:45 Pan-Shun Lau ([email protected]) University of Nevada, Reno, USA Title: The decomposable numerical range of derivations Abstract: Let 1 ≤ k ≤ n be positive integers, G be a subgroup of the symmetric group of order k and χ be an irreducible character of G. The kth generalized numerical range of A ∈ Cn×n associated with G and χ is deﬁned by { } G G ∗ ∈ Cn×k ∗ Wχ (A) = dχ (V AV ): V ,V V = Ik ,

G where dχ is the generalized matrix function associated with G and χ. It is closely related to the decomposable numerical range of derivations. When k = 1, it reduces to the classical G numerical range of A. In the talk, we shall discuss the geometric properties of Wχ (A) such as the convexity and star-shapedness. Co-authors: Nung-Sing Sze (PolyU); Chi-Kwong Li (W&M).

11 • 11:45–12:15 Muneo Ch¯o ([email protected]) Department of Mathematics, Kanagawa University, Japan Title: Numerical ranges of Banach space operators Abstract: Let X be a complex Banach space and X ∗ be the dual space of X . For a bounded linear operator T on X , let the numerical range V (T ) of T is given by

V (T ) = {f(T x):(x, f) ∈ Π },

where Π is deﬁned by Π = { (x, f) ∈ X × X ∗ : ∥f∥ = f(x) = ∥x∥ = 1 }.

In this talk I’ll introduce properties of numerical ranges of T .

References

[1] M. Barra and V. M¨uller,On the essential numerical range, Acta Sci. Math. (Szeged) 71 (2005), 285-298. [2] F.F. Bonsal and J. Duncan, Numerical ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc. Lecture Note Series. 2, 1971. [3] F.F. Bonsal and J. Duncan, Numerical ranges II, London Math. Soc. Lecture Note Series. 10, 1973. [4] M. Ch¯o,Semi-normal operators on uniformly smooth Banach spaces, Glasgow Math. J. 32 (1990), 273-276. [5] M. Ch¯o,Hyponormal operators on uniformly smooth spaces, J. Austral. Math. Soc. 50 (1991), 594-598. [6] M. Ch¯o,Hyponormal operators on uniformly convex spaces, Acta Sci. Math. (Szeged) 55 (1991), 141-147. [7] M. Ch¯oand T. Huruya, A remark on numerical range of semi-hyponormal operators, LMLA, 58 (2010), 711-714. [8] M. Ch¯oand K. Tanahashi, On conjugations for Banach spaces, Sci. Math. Jpn. 81 (2018), 37-45. [9] T. Furuta, Introduction to linear operators, Taylor and Francis, 2001. [10] S. Jung, E. Ko and J. E. Lee, On complex symmetric operators, J. Math. Anal. Appl. 406 (2013), 373-385. [11] H. Motoyoshi, Linear operators and conjugations on a Banach space, to appear in Acta Sci. Math. (Szged).

12 • 14:00–14:30 Hiroshi Nakazato ([email protected]) Department of Mathematics and Physics, Hirosaki Universit, Japan Title: Period matrix of a Riemann surface and the numerical range Abstract: We present a method to compute the period matrix of a Riemann surfacce arising as the boundary generating curve of the numerical range of a matrix. Co-author(s): This talk is based on some joint worls with Professor Mao-Ting Chien.

• 14:30–15:00 Mao-Ting Chien ([email protected]) Department of Mathematics, Soochow University, Taiwan Title: Computing the diameter and width of the numerical range Abstract: The diameter(resp. width) of the numerical range of a matrix is deﬁned to be the largest(resp. smallest) distance of two parallel lines tangent to its boundary. The boundary curve of a numerical range is called a curve of constant width if its diameter and width are equal. In this talk, we provide an algorithm for computing the diameter and width of the numerical range, formulate the diameter of the numerical range of some unitary bordering matrices, and determine the condition for the boundary of the numerical range of certain Toeplitz matrices to be a curve of constant width. Co-author(s): Hiroshi Nakazato, Jie Meng.

13 • 15:00–15:30 Masayo Fujimura ([email protected]) Department of Mathematics, National Defense Academy of Japan, Japan Title: Geometry of ﬁnite Blaschke products: pentagons and pentagrams Abstract: In this talk, I treat two types of curves induced by Blaschke product. For a Blaschke product B of degree d and λ on the unit circle, let ℓλ be the set of lines joining −1 each distinct two preimages in B (λ). The envelope of the family of lines {ℓλ}λ∈∂D is called the interior curve associated with B. In 2002, Daepp, Gorkin, and Mortini proved the interior curve associated with a Blaschke product of degree 3 forms an ellipse. −1 While let Lλ be the set of lines tangent to the unit circle at the d preimages B (λ) and consider the trace of the intersection points of each two elements in Lλ as λ ranges over the unit circle. This trace is called the exterior curve associated with B. The exterior curve associated with a Blaschke product of degree 3 forms a non-degenerate conic. In this talk, I explain the existence of a duality-like geometrical property lies between the interior curve and the exterior curve. Using this property, I create some examples of Blaschke products whose interior curves consist of two ellipses.

z2−0.47 z2−0.2 Figure 1: The envelope indicates the interior curve of B(z) = z 1−0.47z2 1−0.2z2 . The interior curve consists of two ellipses, one is inscribed in the family of pentagons and the other is inscribed in the family of pentagrams.

14 • 16:00–16:30 Patrick X. Rault ([email protected]) Department of Mathematics, University of Nebraska at Omaha, USA Title: Singularities of Base Polynomials and Gau-Wu Numbers Abstract: In 2013, Gau and Wu introduced a unitary invariant, denoted by k(A), of an n × n matrix A, which counts the maximal number of orthonormal vectors xj such that the scalar products ⟨Axj, xj⟩ lie on the boundary of the numerical range W (A). We refer to k(A) as the Gau–Wu number of the matrix A. We write H1 and iH2 for the Hermitian and skew-Hermitian parts of A (respectively), and use them to define the base polynomial F (x, y, t) = det(xH1 + yH2 + tI). In this talk we will take an algebraic-geometric approach and consider the effect of the singularities of the base curve F (x : y : t) = 0, whose dual is the boundary generating curve, to classify k(A). This continues the work of Wang and Wu classifying the Gau-Wu numbers for 3 × 3 matrices. Our focus on singularities is inspired by Chien and Nakazato, who classified W (A) for 4 × 4 unitarily irreducible A with irreducible base curve according to singularities of that curve. When A is a unitarily irreducible n×n matrix, we give necessary conditions for k(A) = 2, characterize k(A) = n, and apply these results to the case of unitarily irreducible 4 × 4 matrices. Co-author(s): Kristin A. Camenga (Houghton College), Louis Deaett (Quinnipiac Uni- versity), Tsvetanka Sendova (Michigan State University), Ilya M. Spitkovsky (New York University Abu Dhabi), Rebekah B. Johnson Yates (Houghton College)

• 16:30–17:00 Michiya Mori ([email protected]) Graduate School of Mathematical Sciences, the University of Tokyo, Japan Title: Order isomorphisms of von Neumann algebras Abstract: I will consider the usual order structure of self-adjoint parts of von Neumann algebras. I will explain the general form of order isomorphisms between intervals of von Neumann algebras. In particular, I will explain that every order isomorphism between the positive cones of von Neumann algebras without commutative direct summands extends to a linear mapping.

15 • 17:00–17:30 An-Bao Xu ([email protected]) College of Mathematics, Physics and Electronic Engineering, Wenzhou University, China Title: Parametrized quasi-soft thresholding operator for compressed sensing and matrix completion Abstract: Compressed sensing and matrix completion are two new approaches to signal acquisition and processing. Even though the two approaches are diﬀerent, there is a close connection between them. In compressed sensing, based on four basic operator, we give a parametrized quasi-soft thresholding operator and its induced algorithm. Further, by updating parametrized quasi-soft thresholding operator in every iteration, the varied para- metric quasi-soft thresholding algorithm is obtained. Then we generalize both algorithms to suit matrix completion. Finally, the convergence of all algorithms are proved, and the numerical results given show that the new algorithms can eﬀectively improve the accuracy to achieve compressed sensing and matrix completion. Co-author(s): Hugo J. Woerdeman.

16 23, June (Sunday)

• 10:00–10:30 Chi-Kwong Li ([email protected]) Department of Mathematics, College of William and Mary, USA Title: Numerical ranges, operator systems, and quantum channels Abstract: We describe some problems and results on numerical ranges related to operator systems associated with quantum channels.

• 10:30–11:00 NatáliaBebiano ([email protected]) Department of Mathematics, University of Coimbra, Portugal Title: The thermodynamics of systems described by non-Hermitian Hamiltonian operators Abstract: The appearance, in quantum physics, of non-Hermitian Hamiltonians possess- ing a discrete real spectrum inspired a remarkable research activity. In this talk we revisit standard concepts of thermodynamics for systems described by a non-Hemitian Hamil- tonian with real eigenvalues. We mainly focus on the standard case where the energy is the unique conserved quantity. However, other conserved quantities may be considered. Numerical range techniques are used. Co-author: Joãoda Providência.

• 11:15–11:45 Seung-Hyeok Kye ([email protected]) Department of Mathematics, Seoul National University, Seoul, Korea Title: Roles of exposed indecomposable positive multi-linear maps in quantum information theory Abstract: Positive multi-linear maps play essential roles to detect multi-partite entanglement in quantum information theory. We need indecomposable positive maps in order to PPT entanglement. We discuss what kinds of map do we need to detect nonzero volume of PPT entanglement. Exposedness arise naturally in this context. We exhibit several examples of exposed indecomposable positive maps in 3 ⊗ 3 and 2 ⊗ 2 ⊗ 2 cases. We also discuss how these maps can be used to study the structures of the convex set consisting of separable states.

17 • 11:45–12:15 G. Ramesh ([email protected]) Department of Mathematics, I. I. T. Hyderabad, Sangareddy, Telangana, India-502 285 Title: On a subclass of norm attaining operators Abstract: A bounded linear operator T : H → H, where H is a Hilbert space, is said to be norm attaining if there exists a unit vector x ∈ H such that ∥T x∥ = ∥T ∥. Let RT denote the set of all reducing subspaces of T . Deﬁne

β(H) := {T ∈ B(H): T |M : M → M is norm attaining for every M ∈ RT }.

In this talk, we discuss properties and structure of positive operators in β(H) and compare with those of absolutely norm attaining operators (AN -operators). Co-author(s): Hiroyuki Osaka, Ritsumeikan University, BKC Campus, Kusatsu, Japan.

• 14:00–14:30 Yongdo Lim ([email protected]) Department of Mathematics, Sungkyunkwan University, Korea Title: Polar decompositions and Aluthge transforms Abstract: We introduce a new polar decomposition on the Lie group of invertible matrices

M = P tUP, t ≠ 1

1+t and the absolute map |M|t := P (the usual polar decomposition is when t = 0). In this talk, we discuss the corresponding Aluthge transform

△ | |λ | |1−λ t,λ(M) := M t Ut(M) M t

and its numerical range. Co-author: Jorge Antezana.

• 14:30–15:00 Yuki Seo ([email protected]) Department of Mathematics Education, Osaka Kyoiku University, Japan Title: Numerical radius inequalities related to the geometric means of negative power Abstract: The norm inequalities related to the geometric means are discussed by many researchers. We discuss numerical radius inequalities related to the geometric means. Though the operator norm is unitarily invariant one, the numerical radius is not so and unitarily similar. In this talk, we show numerical radius inequalities related to the geometric means of negative power for positive invertible operators.

18 • 15:00–15:30 Shigeru Furuichi ([email protected]) Department of Information Science, College of Humanities and Sciences, Nihon University, Japan Title: Generalization and improvements of numerical radius inequalities Abstract: Let B (H) denote the C∗-algebra of all bounded linear operators on a complex Hilbert space H. For A ∈ B (H), let w (A) and ∥A∥ denote the numerical radius and the usual operator norm of A, respectively. It is well known that 1 ∥A∥ ≤ w (A) ≤ ∥A∥ . 2 An improvement of the above inequality has been given by Kittaneh in 2005. It says that for A ∈ B (H), 1 1 ∥A∗A + AA∗∥ ≤ w2 (A) ≤ ∥A∗A + AA∗∥ . 4 2 In this talk, after reviewing recent results containing such inequalities, by using the properties of convex functions, we improve under a certain condition and generalize these inequalities. Our trial to obtain improvements for the previous results depend on our tools of mathematical inequalities so that such an application to numerical radius inequalities is a new approach. Thus we hope to be useful for researchers in the ﬁeld. Meanwhile we study this topic with geometrically convex functions, we obtained interesting scalar inequalities as a by-product. Co-author: Hamid Reza Moradi, Department of Mathematics, Payame Noor University (PNU), Iran, [email protected]

• 16:00–16:30 Jinchuan Hou ([email protected]) Department of Mathematics, Taiyuan University of Technology, China Title: Preservers of numerical radius on Lie products of self-adjoint operators

Abstract: Let H be a complex Hilbert space with dim H ≥ 3, Bs(H) the Lie algebra of all bounded self-adjoint operators on H, and let F : B(H) → [d, ∞] with d ≥ 0 be a radial unitary similarity invariant function. A structure feature for maps ϕ on Bs(H) satisfying

F (ϕ(A)ϕ(B) − ϕ(B)ϕ(A)) = F (AB − BA)(A, B ∈ Bs(H))

is given. As an application of this result, a characterization of the maps on Bs(H) preserving the numerical radius, the maps preserving the p-norm, the maps preserving the pseudo spectral radius are obtained. Furthermore, complete classiﬁcation of the maps on Bs(H) preserving the numerical range and the maps preserving the pseudo spectrum are also achieved. Co-author(s): Qingsen Xu (TYUT).

19 • 16:30–17:00 Ming-Cheng Tsai ([email protected]) General Education Center, Taipei Uni- versity of Technology, TAIWAN Title: Nonsurjective maps between rectangular matrices preserving disjointness, (zero) triple product or norms

Abstract: Let Mm,n be the space of m × n real or complex rectangular matrices. Two ∗ ∗ matrices A, B ∈ Mm,n are disjoint if A B = 0n and AB = 0m. In this talk, a characterization is given for linear maps Φ : Mm,n → Mr,s sending disjoint matrix pairs to disjoint matrix pairs, i.e., A, B ∈ Mm,n being disjoint ensures that Φ(A), Φ(B) ∈ Mr,s being disjoint. The result is used to characterize nonsurjective linear maps that pre- serve JB∗-triple product, or just zero triple product, on rectangular matrices, deﬁned by { } 1 ∗ ∗ A, B, C = 2 (AB C + CB A). The result is also applied to characterize linear maps between rectangular matrix spaces of diﬀerent sizes preserving the Schatten p-norms or the Ky Fan k-norms. Co-author(s): Chi-Kwong Li, Ya-Shu Wang, Ngai-Ching Wong.

• 17:00–17:30 Shuhei Wada ([email protected]) Department of Information and Computer Engineering, National Institute of Technol- ogy(KOSEN), Kisarazu College, Japan. Title: Ando-Hiai type inequalities for operator means and operator perspectives Abstract: When σ is an operator mean in the sense of Kubo-Ando and A, B > 0 are positive invertible operators, the Ando-Hiai inequality is typically stated as follows:

AσB ≤ I ⇒ ApσBp ≤ I (p ≥ 1),

AσB ≥ I ⇒ ApσBp ≥ I (p ≥ 1).

Since the ﬁrst appearance in the case of weighted operator geometric means, Ando-Hiai type inequalities for operator means have been in active consideration, and have taken an important part in recent developments of multivariable operator means, in particular, of multivariable geometric means. We improve the existing Ando-Hiai inequalities for operator means and present new ones for operator perspectives in several ways. We also provide the operator perspective version of the Lie-Trotter formula and consider the extension problem of operator perspectives to non-invertible positive operators. Co-author(s): Fumio Hiai and Yuki Seo.

20 WONRA 2019 Paticipants List

Name Affiliation Country e-mail 1 Kennedy Ayam Ekiah University of Maroua Cameroon 2 Sheriff S. Bah Newton Institute of Technology & Management Gambia 3 Natalia Bebiano University of Coimbra Portugal [email protected] 4 Ssesanga Brian Gulu University Uganda 5 Mao-Ting Chien Soochow University Taiwan [email protected] 6 Didier Roger Chi Nche University of Ngaundere Cameroon [email protected] 7 Muneo Cho Kanagawa University Japan [email protected] 8 Kennett Dela Rosa Drexel University USA [email protected] 9 Nakacwa Faridah Mpigi Vacational & techinical institute Uganda 10 Masayo Fujimura National Defense Academy of Japan Japan [email protected] 11 Shigeru Furuichi Nihon University Japan [email protected] 12 Ramesh Golla IIT India [email protected] 13 Yusaku Goto Ritsumeikan University Japan 14 Osamu Hatori Niigata University Japan [email protected] 15 Fumio Hiai Tohoku University Japan [email protected] 16 Jinchuan Hou Taiyuan University of Technology China [email protected] 17 Masatoshi Ito Maebashi Institute of Technology Japan [email protected] 18 Ssenkaali Julius Lugazi techinical & Engeneering College Uganda 19 Seung-Hyeok Kye Seoul National University Korea [email protected] 20 Pan Shun Lau University of Nevada Reno USA [email protected] 21 Hosoo Lee Jeju National University Korea [email protected] 22 Chi-Kwong Li College of William and Mary USA [email protected] 23 Yongdo Lim Sungkyunkwan University Korea [email protected] 24 Sang K. Mendy Newton Institute of Technology & Management Gambia [email protected] 25 Michiya Mori The University of Tokyo Japan [email protected] 26 Violet Munka Ngwang University of Maroua Cameroon 27 Masaru Nagisa Chiba University Japan [email protected] 28 Hiroshi Nakazato Hirosaki University Japan [email protected] 29 Bbaale Nicholas Masaka Techinical & Business College Uganda 30 Hiromichi Ohno Shinsyu University Japan [email protected] 31 Hiroyuki Osaka Ritsumeikan University Japan [email protected] 32 Edward Poon Embry-Riddle University USA [email protected] 33 Xiaofei Qi Shanxi University China [email protected] 34 Patrick Rault University of Nebraska at Omaha USA [email protected] 35 Takashi Sano Yamagata University Japan [email protected] 36 Yuki Seo Osaka Kyoiku University Japan [email protected] 37 Nassiwa Esther Shammah Buganda Royal Insitute Uganda 38 Moki Smith Beckley University of Ngaundere Cameroon 39 Ilya Spitkovsky New York University Abu Dhabi UAE [email protected] 40 Byaruhanga Stephen Ymca Comprehensive Insititute Kampala Uganda 41 Raymond Nung-Sing Sze The Hong Kong Polytechnic University Hong Kong [email protected] 42 Hiroki Tamura Yamagata University Japan [email protected] 43 Raisei Tomita Ritsumeikan University Japan 44 Yukihiro Tsurumi Ritsumeikan University Japan 45 Ming-Cheng Tsai Taipei University of Technology Taiwan [email protected] 46 Yoich Udagawa Ritsumeikan University Japan National Institute of Technology, 47 Shuhei Wada Japan [email protected] Kisarazu College 48 An-Bao Xu Wenzhou University China [email protected] 49 Takeaki Yamazaki Toyo University Japan [email protected] 50 Kenjiro Yanagi Josai University Japan [email protected] 51 Masahiro Yanagida Tokyo University of Science Japan [email protected]