## Annals of Functional Analysis

### Scattered locally $C^{\ast}$-algebras

Maria Joiţa

#### Abstract

In this article, we introduce the notion of a scattered locally $C^{\ast}$-algebra and we give the conditions for a locally $C^{\ast}$-algebra to be scattered. Given an action $\alpha$ of a locally compact group $G$ on a scattered locally $C^{\ast}$-algebra $A[\tau_{\Gamma}]$, it is natural to ask under what conditions the crossed product $A[\tau_{\Gamma}]\times_{\alpha}G$ 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
Accepted: 30 January 2017
First available in Project Euclid: 12 July 2017

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

Digital Object Identifier
doi:10.1215/20088752-2017-0021

#### 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

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