## Journal of Mathematics of Kyoto University

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

### Invariant averagings of locally compact groups

Djavvat Khadjiev and Abdullah Çavuş

#### 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

**Subjects**

Primary: 43A07: Means on groups, semigroups, etc.; amenable groups

Secondary: 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions

#### 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