Some ergodic properties of multipliers on commutative Banach algebras


Mustafayev H. , Topal H.

TURKISH JOURNAL OF MATHEMATICS, cilt.43, ss.1721-1729, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 43 Konu: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3906/mat-1812-110
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Sayfa Sayıları: ss.1721-1729

Özet

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.