Dominated convergence in measure on semifinite von Neumann algebras and arithmetic averages of measurable operators
type: Item
instance of: scholarly article
title: Dominated convergence in measure on semifinite von Neumann algebras and arithmetic averages of measurable operators
zbMATH Open document ID: 1257.46034
DOI: 10.1134/S0037446612020036
author: A. A. Sabirova
author: Airat Bikchentaev
published in: Siberian Mathematical Journal
publication date: 2012-11-14T00:00:00Z
review text: From the authors' abstract: Given a von Neumann algebra \(M\) with a faithful normal semifinite trace \({\tau}\), the authors prove that each order bounded sequence of \({\tau}\)-compact operators has a subsequence whose arithmetic averages converge in \({\tau}\). They also prove a noncommutative analog of Pratt's lemma for \(L_{1}(M, {\tau})\). They apply the main result to \(L_{p}(M, {\tau})\) with \(0<p \leq 1\) and present some examples that show the necessity of passing to the arithmetic averages as well as the necessity of \({\tau}\)-compactness of the dominant.
Mathematics Subject Classification ID: 46L51
zbMATH DE Number: 6105672
zbMATH Keywords: Hilbert space
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: normal semifinite trace
zbMATH Keywords: measurable operator
zbMATH Keywords: topology of convergence in measure
zbMATH Keywords: spectral theorem
zbMATH Keywords: Banach space
zbMATH Keywords: Banach-Saks property
zbMATH Keywords: arithmetic averages
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
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full work available at URL: s0037446612020036
OpenAlex ID: W1970346284
description: scientific article; zbMATH DE number 6105672