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无限维系统正迹类算子上保持Bregman f-散度映射
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Abstract:
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.
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