## Banach Journal of Mathematical Analysis

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

### Generalized quasidiagonality for extensions

P. W. Ng and Tracy Robin

#### 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 ${C}^{\ast}$-algebras, including certain continuous-scale hereditary ${C}^{\ast}$-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