Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591615 | Journal of Functional Analysis | 2009 | 8 Pages |
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.
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