Continuous invariant averagings

Khadjiev D., Cavus A.

TURKISH JOURNAL OF MATHEMATICS, vol.37, no.5, pp.770-780, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 5
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1112-6
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.770-780
  • Karadeniz Technical University Affiliated: Yes

Abstract

Main results: For every equicontinuous almost periodic linear representation of a group in a complete locally convex space L with the countability property, there exists the unique invariant averaging; it is continuous and is expressed by using the L-valued invariant mean of Bochner and von-Neumann. An analog of Wiener's approximation theorem for an equicontinuous almost periodic linear representation in a locally convex space with the countability property is proved.