Weak amenability of general measure algebras
Volume 111 / 2008
Colloquium Mathematicum 111 (2008), 1-9
MSC: 43A10, 43A62, 43A07.
DOI: 10.4064/cm111-1-1
Abstract
We study the weak amenability of a general measure algebra $M(X)$ on a locally compact space $X$. First we show that not all general measure multiplications are separately weak$^*$ continuous; moreover, under certain conditions, weak amenability of $M(X)^{**}$ implies weak amenability of $M(X)$. The main result of this paper states that there is a general measure algebra $M(X)$ such that $M(X)$ and $M(X)^{**}$ are weakly amenable without $X$ being a discrete topological space.
