## Journal of Mathematics of Kyoto University

### Invariant averagings of locally compact groups

#### Abstract

A definition of an invariant averaging for a linear representation of a group in a locally convex space is given. Main results: A group $H$ is finite if and only if every linear representation of $H$ in a locally convex space has an invariant averaging. A group $H$ is amenable if and only if every almost periodic representation of $H$ in a quasi-complete locally convex space has an invariant averaging. A locally compact group $H$ is compact if and only if every strongly continuous linear representation of $H$ in a quasi-complete locally convex space has an invariant averaging.

#### Article information

Source
J. Math. Kyoto Univ., Volume 46, Number 4 (2006), 701-711.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250281600

Digital Object Identifier
doi:10.1215/kjm/1250281600

Mathematical Reviews number (MathSciNet)
MR2320347

Zentralblatt MATH identifier
1138.43002

#### Citation

Khadjiev, Djavvat; Çavuş, Abdullah. Invariant averagings of locally compact groups. J. Math. Kyoto Univ. 46 (2006), no. 4, 701--711. doi:10.1215/kjm/1250281600. https://projecteuclid.org/euclid.kjm/1250281600