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.
Original language | English (US) |
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Pages (from-to) | 332-339 |
Number of pages | 8 |
Journal | Journal of Functional Analysis |
Volume | 257 |
Issue number | 1 |
DOIs | |
State | Published - Jul 1 2009 |
All Science Journal Classification (ASJC) codes
- Analysis