## Advanced Studies in Pure Mathematics

- Adv. Stud. Pure Math.
- Operator Algebras and Applications, H. Kosaki, ed. (Tokyo: Mathematical Society of Japan, 2004), 19 - 64

### On quasidiagonal $C^*$-algebras

#### Abstract

We give a detailed survey of the theory of quasidiagonal $C^*$-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular we look at what is currently known (and not known) about tensor products, quotients, extensions, free products, etc. of quasidiagonal $C^*$-algebras. We also point out how quasidiagonality is connected to some important open problems.

#### Article information

**Source***Operator Algebras and Applications*, H. Kosaki, ed. (Tokyo: Mathematical Society of Japan, 2004), 19-64

**Dates**

First available in Project Euclid:
1 January 2019

**Permanent link to this document**

https://projecteuclid.org/
euclid.aspm/1546368824

**Digital Object Identifier**

doi:10.2969/aspm/03810019

**Mathematical Reviews number (MathSciNet)**

MR2059800

**Zentralblatt MATH identifier**

1065.46033

**Subjects**

Primary: 46L

Secondary: 46L05: General theory of $C^*$-algebras

#### Citation

Brown, Nathanial P. On quasidiagonal $C^*$-algebras. Operator Algebras and Applications, 19--64, Mathematical Society of Japan, Tokyo, Japan, 2004. doi:10.2969/aspm/03810019. https://projecteuclid.org/euclid.aspm/1546368824