Perturbations of intermediate C*-subalgebras for simple C*-algebras

Shoji Ino, Yasuo Watatani

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study uniform perturbations of intermediate C-subalgebras of inclusions of simple C-algebras. If a unital simple C-algebra has a simple C-subalgebra of finite index, then sufficiently close intermediate C-subalgebras are unitarily equivalent. These intermediate C-subalgebras need not be nuclear. The unitary can be chosen in the relative commutant algebra. An immediate corollary is the following: If the relative commutant is trivial, then the set of intermediate C-subalgebras is a finite set.

Original languageEnglish
Pages (from-to)469-480
Number of pages12
JournalBulletin of the London Mathematical Society
Volume46
Issue number3
DOIs
Publication statusPublished - Jun 2014

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Simple C*-algebras
Subalgebra
Perturbation
Commutant
Unital
Finite Set
Corollary
Trivial
Inclusion
Algebra

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Perturbations of intermediate C*-subalgebras for simple C*-algebras. / Ino, Shoji; Watatani, Yasuo.

In: Bulletin of the London Mathematical Society, Vol. 46, No. 3, 06.2014, p. 469-480.

Research output: Contribution to journalArticle

Ino, Shoji ; Watatani, Yasuo. / Perturbations of intermediate C*-subalgebras for simple C*-algebras. In: Bulletin of the London Mathematical Society. 2014 ; Vol. 46, No. 3. pp. 469-480.
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