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
魏常果,王苍园
摘要(Abstract)：
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。
关键词(KeyWords)： von Neumann代数;σ-弱本质有界;σ-弱可表示
基金项目(Foundation): 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~~
作者(Author): 魏常果,王苍园
DOI: 10.16441/j.cnki.hdxb.20140333
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