Geodesic
Perturbations of AF-Algebras
Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1012-1016

Voir la notice de l'article provenant de la source Cambridge University Press

Let A and B be C*-algebras acting on a Hilbert space H, and let where A 1 is the unit ball in A and d(a, B 1) denotes the distance of a from B 1. 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. 
Phillips, John; Raeburn, Iain. Perturbations of AF-Algebras. Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1012-1016. doi: 10.4153/CJM-1979-093-8
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