Isomorphism of Hilbert modules over stably finite C*-algebras

Details Isomorphism of Hilbert modules over stably finite C*-algebras Isomorphism of Hilbert modules over stably finite C*-algebras

2008-11-06

arxiv.org/abs/0811.0958v1

Mathematics

Operator Algebras

Scientific paper

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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