Ergodic characterizations of character amenability and contractibility of Banach algebras

Abstract

For a nonzero character $\phi$ on a Banach algebra ${\frak A}$, we investigate some relations between $\phi$-amenability of ${\frak A}$ and ergodic theory. As the main result, we give a characterization for $\phi$-amenability of ${\frak A}$ in terms of antirepresentations of ${\frak A}$ on a Banach space.