%0 Journal Article
%T 无限维系统正迹类算子上保持Bregman f-散度映射<br>Maps Preserving Bregman f-Divergence on the Set of Positive Definite Trace Operators of Infinite Dimensional Systems
%A 李田
%A 张艳芳
%A 贺衎
%J Advances in Applied Mathematics
%P 996-1002
%@ 2324-8009
%D 2022
%I Hans Publishing
%R 10.12677/AAM.2022.113107
%X 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。<br />
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 <span>x？xlogx</span>); then we show that these maps are unitary transformations or anti-unitary transformations.
%K 正迹类算子，Bregman f-散度，Umegaki相对熵，保持<br>Positive Definite Trace Operators
%K Bregman f-Divergence
%K Umegaki Relative Entropy
%K Preservers
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=49285