A nonseparable amenable operator algebra which is not isomorphic to a C*-algebra

Abstract

It has been a longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a nonseparable counterexample. The existence of a separable counterexample remains an open problem. We also initiate a general study of unitarizability of representations of amenable groups in C*-algebras and show that our method cannot produce a separable counterexample.

Some improvements

Cited by in corpus (3)

• Rigidity of continuous quotients
• Abelian, amenable operator algebras are similar to C*-algebras
• Obstructions to lifting abelian subalgebras of corona algebras