摘要
设B(H)是复Hilbert空间H上的有界线性算子全体,本文主要研究B(H)上的减偏序遗传子空间的特征,证明了B(H)中的弱算子拓扑闭子空间M是减偏序遗传子空间的充要条件是存在投影P,Q∈B(H),使得M=PB(H)Q.作为应用,给出了B(H)上的长度为1的初等算子保持减偏序的充要条件.
Let B(H) be the set of all bounded linear operators on a complex Hilbert space H. In this paper, we consider the structure of a hereditary subspace with respect to minus partial order in B(H). It is proved that a weak operator topology closed subspace AA in B(H) is hereditary with respect to the minus partial order if and only if there is a pair of projections P and Q in B(H) such that M = PB(H)Q. As an application, we give a sufficient and necessary condition for an elementary operator of length one on B(H) to preserve the minus partial order.
出处
《数学进展》
CSCD
北大核心
2013年第5期701-705,共5页
Advances in Mathematics(China)
基金
国家自然科学基金(No.10971123)
教育部高等学校博士点基金资助课题(No.20090202110001)
关键词
减偏序
遗传子空间
投影
初等算子
minus partial order
hereditary space
projection
elementary operator