### Abstract

Original language | English |
---|---|

Pages (from-to) | 229-256 |

Number of pages | 28 |

Journal | Proceedings of the London Mathematical Society |

Volume | 102 |

Issue number | 2 |

Early online date | 23 Jul 2010 |

DOIs | |

Publication status | Published - 1 Feb 2011 |

### Fingerprint

### Keywords

- C*-algebras
- Hilbert C*-modules
- Cuntz semigroup

### ASJC Scopus subject areas

- Analysis

### Cite this

^{*}-modules over a commutative C

^{*}-algebra.

*Proceedings of the London Mathematical Society*,

*102*(2), 229-256. https://doi.org/10.1112/plms/pdq017

**Hilbert C ^{*}-modules over a commutative C^{*}-algebra.** / Robert, L.; Tikuisis, A.

Research output: Contribution to journal › Article

^{*}-modules over a commutative C

^{*}-algebra',

*Proceedings of the London Mathematical Society*, vol. 102, no. 2, pp. 229-256. https://doi.org/10.1112/plms/pdq017

^{*}-modules over a commutative C

^{*}-algebra. Proceedings of the London Mathematical Society. 2011 Feb 1;102(2):229-256. https://doi.org/10.1112/plms/pdq017

}

TY - JOUR

T1 - Hilbert C*-modules over a commutative C*-algebra

AU - Robert, L.

AU - Tikuisis, A.

PY - 2011/2/1

Y1 - 2011/2/1

N2 - This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fiber dimensions differ sufficiently, relative to the dimension of the spectrum, we show that there is an embedding between the modules. This result continues to hold over recursive subhomogeneous C*-algebras. For certain modules, including all modules over C(X) when dim X = 3, isomorphism and embedding are determined by the restrictions to the sets where the fiber dimensions are constant. These considerations yield results for the Cuntz semigroup, including a computation of the Cuntz semigroup for C(X) when dim X = 3, in terms of cohomological data about X.

AB - This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fiber dimensions differ sufficiently, relative to the dimension of the spectrum, we show that there is an embedding between the modules. This result continues to hold over recursive subhomogeneous C*-algebras. For certain modules, including all modules over C(X) when dim X = 3, isomorphism and embedding are determined by the restrictions to the sets where the fiber dimensions are constant. These considerations yield results for the Cuntz semigroup, including a computation of the Cuntz semigroup for C(X) when dim X = 3, in terms of cohomological data about X.

KW - C-algebras

KW - Hilbert C-modules

KW - Cuntz semigroup

UR - http://www.scopus.com/inward/record.url?scp=79751486109&partnerID=8YFLogxK

U2 - 10.1112/plms/pdq017

DO - 10.1112/plms/pdq017

M3 - Article

VL - 102

SP - 229

EP - 256

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 2

ER -