##### Commutative amenable operator algebras

Abstract: Given an amenable Banach algebra $A$ and a continuous
algebra homomorphism $\phi: A\to B(H)$, with $H$ a Hilbert space, what
can be said about $B$, the closure of $\phi(A)$? It has been
conjectured that $B$ should always be isomorphic to an amenable
C*-algebra. This is known to hold in several natural instances, but
remains open even if we assume $A$ is singly generated.

In this talk I will report on work which shows that the conjecture
holds if $A$ is commutative and $\phi(A)$ is contained in a finite von
Neumann algebra. The proof draws on ideas from the work of several
authors, as well as repeated serendipity. If time permits, I will
mention some questions on amenable subalgebras of $\ell^1$-group
algebras.

Location: TR3, Herschel Building
Date/Time: 17th May 2012, 16:00 - 17:00

Published: 10th January 2012