Perturbations of nuclear C*-algebras

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.

45 pages

References in corpus (3)

• Completely positive maps of order zero
• The nuclear dimension of C*-algebras
• Perturbations of C*-algebraic invariants

Cited by in corpus (18)

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• Forcing axioms and coronas of $C^{\ast }$-algebras
• Perturbations of intermediate C*-subalgebras for simple C*-algebras
• Type II_1 factors satisfying the spatial isomorphism conjecture
• The Cuntz semigroup and stability of close C*-algebras
• Kadison-Kastler stable factors
• An algebra whose subalgebras are characterized by density
• Rigidity Conjectures
• Ulam stability for some classes of C*-algebras
• A non-commutative Amir-Cambern theorem for von Neumann algebras and nuclear $C^{\ast }$-algebras
• Structural properties of close II${}_1$ factors
• CCR and CAR algebras are connected via a path of Cuntz-Toeplitz algebras
• A Kadison Kastler row metric and intermediate subalgebras
• Near inclusions of amenable operator algebras