Analysis and Probability seminar

Abstract: The notion of amenability for locally compact groups, introduced by von Neumann in 1929 in the context of measure theory, is a fundamental concept with equivalent characterizations coming from many different corners of mathematics. In C*-algebraic terms, it is the property that the universal and reduced group C*-algebras coincide canonically. In this talk, we consider a family of Banach *-algebras that sit between L^1(G) and the group C*-algebras: the symmetrized L^p- and p-pseudofunction algebras, F*_{L^p}(G) and F*_{\lambda_p}(G), for 1≤p≤2. We show that a locally compact group is amenable if and only if F*_{L^p}(G) and F*_{\lambda_p}(G) coincide canonically, for 1<p≤2. Furthermore, we characterize amenability in terms of the Banach space dual of F*_{\lambda_p}(G).