Invariant averagings of locally compact groups


Khadjiev D., Cavus A.

JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, vol.46, no.4, pp.701-711, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 4
  • Publication Date: 2006
  • Doi Number: 10.1215/kjm/1250281600
  • Title of Journal : JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY
  • Page Numbers: pp.701-711

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.