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

L. Robert, A. Tikuisis

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)229-256
Number of pages28
JournalProceedings of the London Mathematical Society
Volume102
Issue number2
Early online date23 Jul 2010
DOIs
Publication statusPublished - 1 Feb 2011

Fingerprint

Hilbert C*-module
C*-algebra
Module
Isomorphism
Semigroup
Fiber
Continue
Restriction

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

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

In: Proceedings of the London Mathematical Society, Vol. 102, No. 2, 01.02.2011, p. 229-256.

Research output: Contribution to journalArticle

Robert, L. ; Tikuisis, A. / Hilbert C*-modules over a commutative C*-algebra. In: Proceedings of the London Mathematical Society. 2011 ; Vol. 102, No. 2. pp. 229-256.
@article{1ce4a7ebd95f41439592d2b9ab0d4b04,
title = "Hilbert C*-modules over a commutative C*-algebra",
abstract = "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.",
keywords = "C*-algebras, Hilbert C*-modules, Cuntz semigroup",
author = "L. Robert and A. Tikuisis",
year = "2011",
month = "2",
day = "1",
doi = "10.1112/plms/pdq017",
language = "English",
volume = "102",
pages = "229--256",
journal = "Proceedings of the London Mathematical Society",
issn = "0024-6115",
publisher = "Oxford University Press",
number = "2",

}

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 -