TY - JOUR
T1 - Isomorphism of Hilbert modules over stably finite C*-algebras
AU - Brown, Nathanial P.
AU - Ciuperca, Alin
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (N.P. Brown), [email protected] (A. Ciuperca). 1 N.B. was partially supported by DMS-0554870. 2 A.C. was partially supported by Fields Institute.
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.
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U2 - 10.1016/j.jfa.2008.12.004
DO - 10.1016/j.jfa.2008.12.004
M3 - Article
AN - SCOPUS:64849103775
SN - 0022-1236
VL - 257
SP - 332
EP - 339
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -