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

Keywords

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

ASJC Scopus subject areas

  • Analysis

Fingerprint Dive into the research topics of 'Hilbert C<sup>*</sup>-modules over a commutative C<sup>*</sup>-algebra'. Together they form a unique fingerprint.

  • Cite this