Characterization of amenability by a factorization property of the group von Neumann algebra

We show that the amenability of a locally compact group $G$ is equivalent to a factorization property of $VN(G)$ which is given by $ VN(G) = <VN(G)^*VN(G)>$. This answer partially two problems proposed by Z. Hu and M. Neufang in their article \textit{Distinguishing properties of Arens irregula...

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Bibliographic Details
Main Author Poulin, Denis
Format Journal Article
LanguageEnglish
Published 15.08.2011
Subjects
Mathematics - Functional Analysis
Mathematics - Operator Algebras
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Summary:We show that the amenability of a locally compact group $G$ is equivalent to a factorization property of $VN(G)$ which is given by $ VN(G) = <VN(G)^*VN(G)>$. This answer partially two problems proposed by Z. Hu and M. Neufang in their article \textit{Distinguishing properties of Arens irregularity}, Proc. Amer. Math. Soc. 137 (2009), no. 5, 1753-1761.
DOI:10.48550/arxiv.1108.3020