### 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

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## Cite this

Brown, N. P., & Ciuperca, A. (2009). Isomorphism of Hilbert modules over stably finite C

^{*}-algebras.*Journal of Functional Analysis*,*257*(1), 332-339. https://doi.org/10.1016/j.jfa.2008.12.004