Perturbations of nuclear C*-algebras

Details Perturbations of nuclear C*-algebras Perturbations of nuclear C*-algebras

2009-10-26

arxiv.org/abs/0910.4953v1

Acta Math., 208 (2012), 93-150

Mathematics

Operator Algebras

45 pages

Scientific paper

10.1007/s11511-012-0075-5

Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this conjecture when one algebra is separable and nuclear. We also consider one-sided versions of these notions, and we obtain embeddings from certain near inclusions involving separable nuclear C*-algebras. At the end of the paper we demonstrate how our methods lead to improved characterisations of some of the types of algebras that are of current interest in the classification programme.

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