Banach Journal of Mathematical Analysis

Generalized quasidiagonality for extensions

P. W. Ng and Tracy Robin

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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.

Article information

Source
Banach J. Math. Anal., Volume 13, Number 3 (2019), 582-598.

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1558749977

Digital Object Identifier
doi:10.1215/17358787-2019-0005

Mathematical Reviews number (MathSciNet)
MR3978938

Zentralblatt MATH identifier
07083762

Subjects
Primary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
Secondary: 47A10: Spectrum, resolvent 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20]

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

Citation

Ng, P. W.; Robin, Tracy. Generalized quasidiagonality for extensions. Banach J. Math. Anal. 13 (2019), no. 3, 582--598. doi:10.1215/17358787-2019-0005. https://projecteuclid.org/euclid.bjma/1558749977


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