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) |
|---|---|
| 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 |
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All Science Journal Classification (ASJC) codes
- Analysis
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Isomorphism of Hilbert modules over stably finite C*-algebras. / Brown, Nathanial; Ciuperca, Alin.
In: Journal of Functional Analysis, Vol. 257, No. 1, 01.07.2009, p. 332-339.Research output: Contribution to journal › Article
TY - JOUR
T1 - Isomorphism of Hilbert modules over stably finite C*-algebras
AU - Brown, Nathanial
AU - Ciuperca, Alin
PY - 2009/7/1
Y1 - 2009/7/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=64849103775&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=64849103775&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2008.12.004
DO - 10.1016/j.jfa.2008.12.004
M3 - Article
AN - SCOPUS:64849103775
VL - 257
SP - 332
EP - 339
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -