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arXiv · 1306.1915

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

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.

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Shoji Ino, Yasuo Watatani. 2013-06-08. Perturbations of intermediate C*-subalgebras for simple C*-algebras. https://doi.org/10.1112/blms%2Fbdu001

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