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.
Abstract. In this paper, we study uniform perturbations of von Neumann subalgebras of a von Neumann algebra. Let M and N be von Neumann subalgebras of a von Neumann algebra with nite probabilistic index in the sense of Pimsner-Popa. If M and N are su ciently close, then M and N are unitarily equivalent. e implementing unitary can be chosen as being close to the identity.
In this paper, we study uniform perturbations of von Neumann subalgebras of a von Neumann algebra. Let N and M be von Neumann subalgebras of a von Neumann algebra with finite probabilistic index in the sense of Pimsner-Popa. If N and M are sufficiently close, then N and M are unitarily equivalent. The implementing unitary can be chosen as being close to the identity.
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