摘要
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.
出处
《华东师范大学学报(自然科学版)》
CAS
CSCD
1996年第1期6-11,共6页
Journal of East China Normal University(Natural Science)
关键词
希尔伯特空间
贝尔曼不等式
K-可换性
K-正规性
real self-adjoint operators, normal Trace class, k-commutal,k-commutant, k-hyponormal, k-cohyponormal)