Perturbations of nuclear C*-algebras

Erik Christensen; Allan Sinclair; Roger Smith; Stuart White; Wilhelm Winter

doi:10.1007/s11511-012-0075-5

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arXiv · 0910.4953

Perturbations of nuclear C*-algebras

Erik Christensen·Allan Sinclair·Roger Smith·Stuart White·Wilhelm Winter

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Abstract

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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Erik Christensen, Allan Sinclair, Roger Smith, Stuart White, Wilhelm Winter. 2009-10-26. Perturbations of nuclear C*-algebras. https://doi.org/10.1007/s11511-012-0075-5

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