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July 2019 Generalized quasidiagonality for extensions
P. W. Ng, Tracy Robin
Banach J. Math. Anal. 13(3): 582-598 (July 2019). DOI: 10.1215/17358787-2019-0005

Abstract

We generalize the notion of quasidiagonality, for extensions, allowing for the case where the canonical ideal has few projections. We prove that the pointwise-norm limit of generalized quasidiagonal extensions is generalized quasidiagonal. We also provide a K-theory sufficient condition for generalized quasidiagonality of certain extensions of simple continuous-scale C-algebras, including certain continuous-scale hereditary C-subalgebras of the stabilized Jiang–Su algebra.

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P. W. Ng. Tracy Robin. "Generalized quasidiagonality for extensions." Banach J. Math. Anal. 13 (3) 582 - 598, July 2019. https://doi.org/10.1215/17358787-2019-0005

Information

Received: 28 September 2018; Accepted: 3 January 2019; Published: July 2019
First available in Project Euclid: 25 May 2019

zbMATH: 07083762
MathSciNet: MR3978938
Digital Object Identifier: 10.1215/17358787-2019-0005

Subjects:
Primary: 46L80
Secondary: 47A10 , 47A53

Keywords: $C^{*}$-algebras , $KK$-theory , extension theory , multiplier algebras , Weyl–von Neumann–Berg theorem

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.13 • No. 3 • July 2019
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