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

Shoji Ino; Yasuo Watatani

doi:10.1112/blms/bdu001

Perturbations of intermediate C-subalgebras for simple C-algebras

Operator Algebras 2017-05-17 v1

Authors: Shoji Ino , Yasuo Watatani

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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 simple intermediate C*-subalgebras are unitarily equivalent. These C*-subalgebras need not to be nuclear. The unitary can be chosen in the relative commutant algebra. An imediate corollary is the following: If the relative commutant is trivial, then the set of intermediate C*-subagebras is a finite set.

Keywords

C*-algebras intermediate subalgebras uniform perturbations finite index unitary equivalence relative commutant

Cite

@article{arxiv.1306.1915,
  title  = {Perturbations of intermediate C*-subalgebras for simple C*-algebras},
  author = {Shoji Ino and Yasuo Watatani},
  journal= {arXiv preprint arXiv:1306.1915},
  year   = {2017}
}

Comments

10 pages