## Annals of Functional Analysis

- Ann. Funct. Anal. (2018), 11 pages.

### Scattered locally ${C}^{*}$-algebras

#### Abstract

In this article, we introduce the notion of a scattered locally ${C}^{*}$-algebra and we give the conditions for a locally ${C}^{*}$-algebra to be scattered. Given an action $\alpha $ of a locally compact group $G$ on a scattered locally ${C}^{*}$-algebra $A\left[{\tau}_{\Gamma}\right]$, it is natural to ask under what conditions the crossed product $A\left[{\tau}_{\Gamma}\right]{\times}_{\alpha}G$ is also scattered. We obtain some results concerning this question.

#### Note

The current version of this article, posted on 9 August 2017, supersedes the original advance publication version posted on 12 July 2017. The author’s original terminology has been restored.

#### Article information

**Source**

Ann. Funct. Anal. (2018), 11 pages.

**Dates**

Received: 12 October 2016

Accepted: 30 January 2017

First available in Project Euclid: 12 July 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.afa/1499824814

**Digital Object Identifier**

doi:10.1215/20088752-2017-0021

**Subjects**

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

Secondary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20] 46L85: Noncommutative topology [See also 58B32, 58B34, 58J22]

**Keywords**

locally $C^{\ast}$-algebras scattered locally $C^{\ast}$-algebras crossed product of locally $C^{\ast}$-algebras

#### Citation

Joiţa, Maria. Scattered locally $C^{\ast}$ -algebras. Ann. Funct. Anal., advance publication, 12 July 2017. doi:10.1215/20088752-2017-0021. https://projecteuclid.org/euclid.afa/1499824814