Regularity for stably projectionless, simple C*-algebras

Aaron Peter Tikuisis

Research output: Contribution to journalArticle

5 Citations (Scopus)
4 Downloads (Pure)

Abstract

This paper explores the following regularity properties and their relationships for simple, not-necessarily-unital C*-algebras:
(i) Jiang-Su stability,
(ii) unperforation in the Cuntz semigroup, and
(iii) slow dimension growth (applying only in the case that the C*-algebra is approximately subhomogeneous).
An example is given of a simple, separable, nuclear, stably projectionless C*-algebra whose Cuntz semigroup is not almost unperforated. This example is in fact approximately subhomogeneous. It is also shown that, in contrast to this example, when an approximately subhomogeneous simple C*-algebra has slow dimension growth, its Cuntz semigroup is necessarily almost unperforated.
Original languageEnglish
Pages (from-to)1382–1407
Number of pages26
JournalJournal of Functional Analysis
Volume263
Issue number5
Early online date18 Jun 2012
DOIs
Publication statusPublished - 1 Sep 2012

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Simple C*-algebras
C*-algebra
Semigroup
Regularity
Regularity Properties
Unital

Keywords

  • Stably projectionless C*-algebras
  • Cuntz semigroup
  • Jiang-Su algebra
  • approximately subhomogeneous C*-algebras
  • slow dimension growth

ASJC Scopus subject areas

  • Analysis

Cite this

Regularity for stably projectionless, simple C*-algebras. / Tikuisis, Aaron Peter.

In: Journal of Functional Analysis, Vol. 263, No. 5, 01.09.2012, p. 1382–1407.

Research output: Contribution to journalArticle

Tikuisis, Aaron Peter. / Regularity for stably projectionless, simple C*-algebras. In: Journal of Functional Analysis. 2012 ; Vol. 263, No. 5. pp. 1382–1407.
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