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Perturbations of nuclear \(C^*\)-algebras. (English) Zbl 1252.46047

Let \(H\) be a Hilbert space, and let \(A\) and \(B\) be \(C^*\)-subalgebras of \(\mathbb B(H)\). The question raised by Kadison and Kastler asks if \(A\) and \(B\) are isomorphic, provided they are close (with respect to the Hausdorff distance between unit balls). A positive answer is known in some special cases, but in general the answer is negative [M. D. Choi and E. Christensen, Bull. Lond. Math. Soc. 15, 604–610 (1983; Zbl 0541.46046)]. The paper under review answers Kadison and Kastler’s question positively when \(A\) is separable and nuclear.
For the one-sided situation of near inclusions, it is shown that if \(A\) is nearly contained in \(B\), then there is an embedding \(A\hookrightarrow B\) under the assumption that \(A\) is separable and has finite nuclear dimension.

MSC:

46L05 General theory of \(C^*\)-algebras
46L35 Classifications of \(C^*\)-algebras

Citations:

Zbl 0541.46046
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References:

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