2007
DOI: 10.1007/s00208-007-0129-8
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$${\mathcal{C}}_{0}$$ (X)-algebras, stability and strongly self-absorbing $${\mathcal{C}}^{*}$$ -algebras

Abstract: We study permanence properties of the classes of stable and so-called D-stable C * -algebras, respectively. More precisely, we show that a C 0 (X )-algebra A is stable if all its fibres are, provided that the underlying compact metrizable space X has finite covering dimension or that the Cuntz semigroup of A is almost unperforated (a condition which is automatically satisfied for C * -algebras absorbing the Jiang-Su algebra Z tensorially). Furthermore, we prove that if D is a K 1 -injective strongly self-absor… Show more

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Cited by 60 publications
(97 citation statements)
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“…-The C * -algebra A is D-stable by [7]. By Lemma 3.8, Proposition 3.7 and the compactness of X, for any finite set F ⊂ A and any ε > 0 there is an (F, ε, D)-approximation of A.…”
Section: Proving the Main Result: The First Approachmentioning
confidence: 97%
See 2 more Smart Citations
“…-The C * -algebra A is D-stable by [7]. By Lemma 3.8, Proposition 3.7 and the compactness of X, for any finite set F ⊂ A and any ε > 0 there is an (F, ε, D)-approximation of A.…”
Section: Proving the Main Result: The First Approachmentioning
confidence: 97%
“…In this section we give a proof of Theorem 1.1 which follows ideas of [3] and relies on the main absorption result Theorem 4.6 of [7] and on [5, Theorem 2.2]:…”
Section: Proving the Main Result: The First Approachmentioning
confidence: 99%
See 1 more Smart Citation
“…As noted in [7,Section 1], every C * -algebra is a C 0 (X)-algebra, typically in many ways. C 0 (X)-algebras have been studied in [3,8,13,14,15,20,28]. In [6, Section 1], we saw that if A is a C 0 (X)-algebra then corresponding to each x ∈ X there are two natural ideals H x and J x in M(A) which one might hope would be equal but in fact need not be so.…”
Section: Introductionmentioning
confidence: 99%
“…Example 4.8 of [2] exhibits a sequence (B j ) j∈N of unital separable C * -algebras with the following property: there are projections e, f ∈…”
mentioning
confidence: 99%