A properly infinite Banach $*$-algebra with a non-zero, bounded trace
Volume 155 / 2003
Studia Mathematica 155 (2003), 107-129
MSC: Primary 46K05; Secondary 43A20, 46H20, 16N20.
DOI: 10.4064/sm155-2-2
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.
