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Carrión, José R.; Pasnicu, Cornel

Approximations of \(C^{*}\)-algebras and the ideal property. (English) Zbl 1139.46040

J. Math. Anal. Appl. 338, No. 2, 925-945 (2008).
Summary: We introduce several classes of \(C^{*}\)-algebras (using local approximations by “nice” \(C^{*}\)-algebras), that generalize the \(AH\) algebras, among others. We initiate their study, proving mainly results about the ideal property, but also about the ideals generated by their projections, the real rank zero, the weak projection property, minimal tensor products, extensions, quasidiagonal extensions, ideal structure, the largest ideal with the ideal property and short exact sequences. Some of the previous results of the second named author are generalized.

Cited in 5 Documents

MSC:

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

Keywords:

\(C^{*}\)-algebra; local approximation; ideal generated by projections; ideal property; \(LS\) algebra; minimal tensor product; extension; quasidiagonal extension; \(WLB\) algebra; weak projection property; real rank zero; Riesz decomposition property; \(SLB\) algebra; largest ideal with the ideal property
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References:

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