A properly infinite Banach *-algebra with a non-zero, bounded trace

Dales, H. G. and Laustsen, Niels J. and Read, Charles J. (2003) A properly infinite Banach *-algebra with a non-zero, bounded trace. Studia Mathematica, 155 (2). pp. 107-129. ISSN 0039-3223

Abstract

A properly infinite C-algebra has no non-zero traces. We construct properly infinite Banach -algebras with non-zero, bounded traces, and show that there are even such algebras which are fairly \close" to the class of C algebras, in the sense that they can be hermitian or -semisimple.