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Perturbations of AF-Algebras

Published online by Cambridge University Press:  20 November 2018

John Phillips  and
Iain Raeburn
John Phillips
Affiliation:
Dalhousie University, Halifax, Nova Scotia
Iain Raeburn
Affiliation:
University of New South Wales, Kensington, Australia
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Let A and B be C*-algebras acting on a Hilbert space H, and let

where A1 is the unit ball in A and d(a, B1) denotes the distance of a from B1. We shall consider the following problem: if ‖A – B‖ is sufficiently small, does it follow that there is a unitary operator u such that uAu* = B?

Such questions were first considered by Kadison and Kastler in [9], and have received considerable attention. In particular in the case where A is an approximately finite-dimensional (or hyperfinite) von Neumann algebra, the question has an affirmative answer (cf [3], [8], [12]). We shall show that in the case where A and B are approximately finite-dimensional C*-algebras (AF-algebras) the problem also has a positive answer.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 5 , 01 October 1979 , pp. 1012 - 1016
Copyright
Copyright © Canadian Mathematical Society 1979

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