Unitarizability, extensions, and amenable operator algebras

Yemon Choi (Lancaster University)

Thursday 31st March 16:00-17:00 Maths 311B

Abstract

There is a closed subalgebra of $\ell^\infty\otimes M_2$ which is
amenable, yet is not Banach-algebra-isomorphic to any C*-algebra; the
non-isomorphism is witnessed by the failure to be "unitarizable" of
certain bounded subgroups of matrix corona algebras. It remains an
open question whether similar "counterexamples" can be found inside
$C(K)\otimes M_d$ for metrizable $K$. We report on some work in
progress, joint with B. Green (Lancaster), investigating what can be
said when $K$ has finite Cantor-Bendixson rank.