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
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。
Abstract: 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.
文章引用：李田, 张艳芳, 贺衎. 无限维系统正迹类算子上保持Bregman f-散度映射[J]. 应用数学进展, 2022, 11(3): 996-1002. https://doi.org/10.12677/AAM.2022.113107

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