ERGODIC PROPERTIES OF CONVOLUTION OPERATORS IN GROUP ALGEBRAS


Mustafayev H. , Topal H.

COLLOQUIUM MATHEMATICUM, vol.165, no.2, pp.321-340, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 165 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.4064/cm8214-6-2020
  • Title of Journal : COLLOQUIUM MATHEMATICUM
  • Page Numbers: pp.321-340

Abstract

Let G be a locally compact abelian group and let L-1 (G) and M(G) be respectively the group algebra and the convolution measure algebra of G. For mu is an element of M(G), let T(mu)f = mu * f be the convolution operator on L-1(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, where mu(n) denotes the nth convolution power of mu. We study some ergodic properties of the convolution operator T-mu, in the case when mu is power bounded. We also present some results concerning almost everywhere convergence of the sequence {T(mu)(n)f} in L-1 (G).