Some ergodic properties of multipliers on commutative Banach algebras

Authors

HEYBETKULU MUSTAFAYEV
HAYRİ TOPAL

DOI

10.3906/mat-1812-110

Abstract

A commutative semisimple regular Banach algebra $A$ with the Gelfand space $ \Sigma _{A}$ is called a Ditkin algebra if each point of $\Sigma _{A}\cup \left\{ \infty \right\} $ 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 $\left\{ \varphi \in A^{\ast }:T^{\ast }\varphi =\varphi \right\} $ is finite dimensional if and only if \textnormal{card}$\mathcal{F}_{T}$ is finite, where $\mathcal{F}_{T}=\left\{ \gamma \in \Sigma _{A}:\widehat{T}\left( \gamma \right) =1\right\} $ and $ \widehat{T}$ is the Helgason-Wang representation of $T.$

Keywords

Commutative Banach algebra, multiplier, Choquet-Deny theorem

First Page

1721

Last Page

1729

Recommended Citation

MUSTAFAYEV, HEYBETKULU and TOPAL, HAYRİ (2019) "Some ergodic properties of multipliers on commutative Banach algebras," Turkish Journal of Mathematics: Vol. 43: No. 3, Article 45. https://doi.org/10.3906/mat-1812-110
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/45