σ-弱本质有界函数和σ-弱可表示算子  

σ-Weakly Essentially Bounded Functions andσ-Weakly Representable Operators

作　　者：魏常果[1] 王苍园 

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2016年第10期135-138,共4页Periodical of Ocean University of China

基　　金：山东省自然科学基金项目(ZR2011AM003);国家自然科学基金项目(11171315)资助~~

摘　　要：本文引入了σ-弱本质有界算子函数及σ-弱可表示;证明了L(Ω,M)中的元素都能表示成Ω上的σ-弱可列可加算子测度,即存在等距映射将L(Ω,M)等距嵌入Ba(R)中。还刻画了L(Ω,M)上线性算子和线性泛函的性质;最后证明了L(Ω,μ)上算子T为σ-弱可表示算子的充要条件。This paper introduces theσ-weakly essentially bounded functions andσ-weakly representable operators.Let Mbe a von Neumann algebra,Xbe any set and Rbe aσ-field of subsets of X.An operator valued measureμon Ris a map fromRinto the finitely additive subsets of M.Let{En}be a family of any mutually disjoint subsets of R,Ebe the union.Ifμis countably additive on{En},with respect to theσ-weakly operator topology,thenμis calledσ-weakly countably additive measure.Everyσ-weakly integrable operator valued function in L（Ω,M）can be represented to be aσ-weakly countably additive measure onΩ,i.e.there exists an isometric embedding fromL（Ω,M）into Ba（R）.The space of normal linear functionals on Mcan be isometrically embedded into L（Ω,M）^＊.And there is also an isometry fromL∞（Ω,μ）into B（L（Ω,M）;M）.The equivalent characterization of aσ-weakly representable operator is given at the end of this paper.

关 键 词：von NEUMANN代数 σ-弱本质有界 σ-弱可表示 

分 类 号：O177.1[理学—数学]