Amenability for dual Banach algebras

Abstract

We define a Banach algebra ${{\mathfrak A}}$ to be dual if ${{\mathfrak A}} = ({{\mathfrak A}}_\ast )^\ast $ for a closed submodule ${{\mathfrak A}}_\ast $ of ${{\mathfrak A}}^\ast $. The class of dual Banach algebras includes all $W^\ast $-algebras, but