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2015•Canadian Mathematical BulletinOpen access

Perturbations of Von Neumann Subalgebras With Finite Index

Shoji Ino

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Abstract

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

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

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Available abstract

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

Key concepts: Von Neumann algebra, Mathematics, Von Neumann architecture, Abelian von Neumann algebra, Affiliated operator, Unitary state, Pure mathematics, Von Neumann's theorem

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