## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On $\phi$-ergodic property of Banach modules

Mehdi Nemati

#### Abstract

Let ${\mathcal A}$ be a Banach algebra and let $\phi$ be a non-zero character on ${\mathcal A}$. We introduce the notion of $\phi$-ergodic property for a Banach right ${\mathcal A}$-module $X$. This concept considerably generalizes the existence of $\phi$-means of norm one on ${\mathcal A}^*$. We also show that the $\phi$-ergodic property of $X$ is related to some other properties such as a Hahn-Banach type extension property and the existence of $\phi$-means of norm one on a certain subspace of ${\mathcal A}^*$. Finally, we give some characterizations for $\phi$-amenability of a Banach algebra in terms of its closed ideals.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 4 (2015), 655-668.

Dates
First available in Project Euclid: 18 November 2015

https://projecteuclid.org/euclid.bbms/1447856065

Digital Object Identifier
doi:10.36045/bbms/1447856065

Mathematical Reviews number (MathSciNet)
MR3429177

Zentralblatt MATH identifier
1338.46059

#### Citation

Nemati, Mehdi. On $\phi$-ergodic property of Banach modules. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 4, 655--668. doi:10.36045/bbms/1447856065. https://projecteuclid.org/euclid.bbms/1447856065