Isomorphism of Hilbert modules over stably finite C*-algebras
Operator Algebras
2008-11-07 v1
Abstract
It is shown that if A is a stably finite C*-algebra and E is a countably generated Hilbert A-module, then E gives rise to a compact element of the Cuntz semigroup if and only if E is algebraically finitely generated and projective. It follows that if E and F are equivalent in the sense of Coward, Elliott and Ivanescu (CEI) and E is algebraically finitely generated and projective, then E and F are isomorphic. In contrast to this, we exhibit two CEI-equivalent Hilbert modules over a stably finite C*-algebra that are not isomorphic.
Cite
@article{arxiv.0811.0958,
title = {Isomorphism of Hilbert modules over stably finite C*-algebras},
author = {Nathanial P. Brown and Alin Ciuperca},
journal= {arXiv preprint arXiv:0811.0958},
year = {2008}
}