### 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

### Cite this

^{*}-algebras.

*Journal of Functional Analysis*,

*257*(1), 332-339. https://doi.org/10.1016/j.jfa.2008.12.004

}

^{*}-algebras',

*Journal of Functional Analysis*, vol. 257, no. 1, pp. 332-339. https://doi.org/10.1016/j.jfa.2008.12.004

**Isomorphism of Hilbert modules over stably finite C ^{*}-algebras.** / Brown, Nathanial; Ciuperca, Alin.

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 -

^{*}-algebras. Journal of Functional Analysis. 2009 Jul 1;257(1):332-339. https://doi.org/10.1016/j.jfa.2008.12.004