A bicommutant theorem for dual Banach algebras

Matthew Daws

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arXiv · 1001.1146

A bicommutant theorem for dual Banach algebras

Matthew Daws

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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 $π:\mc A\to\mc B(E)$ such that $π(\mc A)$ equals its own bicommutant.

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Matthew Daws. 2010-01-07. A bicommutant theorem for dual Banach algebras. https://arxiv.org/abs/1001.1146

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