Invariant averagings of locally compact groups

• Autores: Djavvat Khadjiev, Abdullah Çavus
• Localización: Journal of mathematics of Kyoto University, ISSN 0023-608X, Vol. 46, Nº 4, 2006, págs. 701-711
• Idioma: inglés
• DOI: 10.1215/kjm/1250281600
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• Resumen

  • 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.