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. 1 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 University Restaurant (1F) and Shop (2F) open on Saturday 8:30—14:00. 9 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 2 W (A)n@W (A), where A 2 3×3 C is a normal matrix with noncollinear eigenvalues, determines a unique number µ2 2 W (A) so that fµ1; µ2g 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 2 W (A) in the interior of one of the quadrants formed by the diagonals of W (A), we prove that if fµ1; µ2g 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 2 Cn×n associated with G and χ is defined by n o G G ∗ 2 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 .