摘要
设初等算子E(X)=∑AiXBi,定义E*(X)=∑Ai*XBi*.我们证明了EE*=E*E当且仅当{Ai}和{Bi}都是交换的正规算子族,从而回答了由D.Keckic提出的关于初等算子正规性的开问题.我们还给出了E=E*的充分必要条件.
Given an elementary operator E(X) = AiXBi, we define E* (X) = Ai*XBi*. Inthis note, we prove that EE* = E*E if and only if {Ai} and {Bi} are commuting families of normal perators, which answers the question on normality of elementary operators proposed by D. Keckic. We also give a necessary and sufficient condition that assures that E =E*.
出处
《应用泛函分析学报》
CSCD
2002年第2期118-123,共6页
Acta Analysis Functionalis Applicata
关键词
初等算子
正规性
正规算子
elementary operator
normality
normal operator
