ON THE CONVERGENCE OF ITERATES OF CONVOLUTION OPERATORS IN BANACH SPACES


Mustafayev H.

MATHEMATICA SCANDINAVICA, vol.126, no.2, pp.339-366, 2020 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 126 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.7146/math.scand.a-119601
  • Title of Journal : MATHEMATICA SCANDINAVICA
  • Page Numbers: pp.339-366

Abstract

Let G be a locally compact abelian group and let M(G) be the measure algebra of G. A measure mu is an element of M(G) is said to be power bounded if sup(n >= 0) parallel to mu(n)parallel to(1) < infinity. Let T = {T-g : g is an element of G} be a bounded and continuous representation of G on a Banach space X. For any mu is an element of M(G), there is a bounded linear operator on X associated with mu, denoted by T-mu, which integrates T-g with respect to mu. In this paper, we study norm and almost everywhere behavior of the sequences {T-mu(n) x} (x is an element of X) in the case when mu, is power bounded. Some related problems are also discussed.