A BICOMMUTANT THEOREM FOR DUAL BANACH ALGEBRAS

Abstract

A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak∗-continuous. We show that given a unital dual Banach algebra $\mc A$, we can find a reflexive Banach space E, and an isometric, weak∗-weak∗-continuous homomorphism $\pi:\mc A\to\mc B(E)$ such that $\pi(\mc A)$ equals its own bicommutant.