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

Denis Poulin

paper

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

arXiv:1108.3020

Abstract

We show that the amenability of a locally compact group $G$ is equivalent to a factorization property of $V N (G)$ which is given by $V N (G) =< V N (G)^{*} V N (G) >$ . 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.