University of New Hampshire University of New Hampshire Scholars' Repository Doctoral Dissertations Student Scholarship Fall 2018 UNITARILY INVARIANT NORMS ON FINITE VON NEUMANN ALGEBRAS Haihui Fan University of New Hampshire, Durham Follow this and additional works at: https://scholars.unh.edu/dissertation Recommended Citation Fan, Haihui, "UNITARILY INVARIANT NORMS ON FINITE VON NEUMANN ALGEBRAS" (2018). Doctoral Dissertations. 2418. https://scholars.unh.edu/dissertation/2418 This Dissertation is brought to you for free and open access by the Student Scholarship at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact
[email protected]. UNITARILY INVARIANT NORMS ON FINITE VON NEUMANN ALGEBRAS BY HAIHUI FAN BS, Mathematics, East China University of Science and Technology, China, 2008 MS, Mathematics, University of New Hampshire, United States, 2016 DISSERTATION Submitted to the University of New Hampshire in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics September 2018 ALL RIGHTS RESERVED ©2018 Haihui Fan This dissertation has been examined and approved in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics by: Dissertation Director, Donald Hadwin, Professor of Mathematics Eric Nordgren, Professor of Mathematics Rita Hibschweiler, Professor of Mathematics Junhao Shen, Professor of Mathematics Mehmet Orhon, Lecturer of Mathematics on 07/31/2018. Original approval signatures are on file with the University of New Hampshire Graduate School. iii ACKNOWLEDGMENTS I am deeply indebted to my advisor Professor Donald Hadwin for showing me so much math- ematics, and encouraging me in this research.