Comparison of topologies on *-algebras of locally measurable operators

2010/01/11 by Vladimir Chilin, V. I. Chilin, Chilin, V. I. +3
Mathematics · Physics and Astronomy · #06F25 #06F30 #46L50 #47D25 #47D40 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Mechanics and Applications #math.OA #msc:06F25 #msc:06F30 #msc:46L50 #msc:47D25 #msc:47D40

paper · pdf · doi:10.48550/arxiv.1001.1651

21 pages

arxiv created 2010/01/11 · openalex publication_date 2010/01/11 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the locally measure topology t(M) on the *-algebra LS(M) of all locally measurable operators affiliated with a von Neumann algebra M. We prove that t(M) coincides with the (o)-topology on LS_h(M)=\T∈ LS(M): T^*=T\ if and only if the algebra M is σ-finite and a finite algebra. We study relationships between the topology t(M) and various topologies generated by faithful normal semifinite traces on M.

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