关于k—可换性与k—正规性

On k-commulality and k-normality

本文证明了对实自共轭迹类算子有Ｔｒ（（ＡＢ）２ｎ）≤Ｔｒ（Ａ２ｎＢ２ｎ），即ｋ＝２ｎ情形下的Ｈｉｌｂｅｒｔ空间中Ｂｅｌｌｍａｎ不等式；定义了ｋ－换位子，讨论其若干性质；并给出Ｔｒ（ＡＡ）２＝Ｔｒ（Ａ２Ａ）的充要条件，等价定义了正常这类算子。

Bellman Inequality Tr((AB)2n )≤Tr(A2n B2n) on Hilbert space is proofed to be valid for operators belonging to the real self-adjoint trace class. k-commutant is defined and some of its properties are discussed. A sufficient and necessary condition for Tr((AA)2)=Tr(A2 A2) is given and the normal trace class operatess are equivalently defined.