关于von Neumann代数上的几种算子拓扑的研究

A Study of Several Operator Topologies on von Neumann Algebras

设A是作用于Hilbert空间ℋ上的C∗-代数,B(K)是作用于Hilbert空间ℋ上的von Neumann代数。本文讨论了C∗-代数A到von Neumann代数B(K)的线性映射在σ-强算子拓扑和σ-弱算子拓扑下的连续性。

LetAbe theC∗-algebra acting on the Hilbert spaceℋ, andB(K)be the von Neumann algebra acting on the Hilbert spaceℋ. In this paper, we discuss the continuity of linear maps fromC∗-algebraAto von Neumann algebraB(K)inσ-strong operator topology andσ-weak operator topology.