无限维系统正迹类算子上保持Bregman f-散度映射  

Maps Preserving Bregman f-Divergence on the Set of Positive Definite Trace Operators of Infinite Dimensional Systems

作　　者：李田 张艳芳 贺衎 

机构地区：[1]太原理工大学,数学学院,山西 太原

出　　处：《应用数学进展》2022年第3期996-1002,共7页Advances in Applied Mathematics

摘　　要：设H为无限维的可分Hilbert空间,令PTr(H)表示H上所有的正定的迹类算子组成的集合。该文主要研究了无限维的可分Hilbert空间H上正迹类算子的保持问题,给出了PTr(H)上保持满足某些条件的可微凸函数对应的Bregman f-散度和Umegaki相对熵(函数x⟼xlogx对应的Bregman散度)的双射的完全刻画。Let H be an infinite separable Hilbert space and PTr(H) represent the set of all positive trace operators on H. In this paper, we characterize the bijective maps on PTr(H) preserving Bregman f-divergence where f is a differentiable convex function satisfying certain conditions and Umegaki relative entropy (Bregman divergence corresponding to function x⟼xlogx);then we show that these maps are unitary transformations or anti-unitary transformations.

关 键 词：正迹类算子 Bregman f-散度 Umegaki相对熵 保持 

分 类 号：O177[理学—数学]