Dual Banach Algebras

Abstract

A dual Banach algebra is a Banach algebra that is also a dual Banach space such that multiplication is separately weak$^*$ continuous. Examples of dual Banach algebras are, among others, von Neumann algebras, the measure algebra M(G). and the Fourier–Stieltjes algebra B(G) of a locally compact group G, or the algebras $\mathcal {B}(E)$ of all bounded linear operators on a reflexive Banach space E.