Some ergodic properties of multipliers on commutative Banach algebras


Mustafayev H. , Topal H.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.3, pp.1721-1729, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1812-110
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.1721-1729

Abstract

A commutative semisimple regular Banach algebra Sigma(A) with the Gelfand space Sigma(A) is called a Ditkin algebra if each point of Sigma(A) boolean OR {infinity} is a set of synthesis for A. Generalizing the Choquet-Deny theorem, it is shown that if T is a multiplier of a Ditkin algebra A, then {phi is an element of A* : T* phi = phi} is finite dimensional if and only if card F-T is finite, where F-T = {gamma is an element of Sigma(A) : (T) over cap (gamma) = 1} and (T) over cap is the Helgason-Wang representation of T.