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Journal Article

A BICOMMUTANT THEOREM FOR DUAL BANACH ALGEBRAS

Matthew Daws
Mathematical Proceedings of the Royal Irish Academy
Vol. 111A, No. 1 (OCTOBER 2011), pp. 21-28
Stable URL: http://www.jstor.org/stable/23208667
Page Count: 8

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Abstract

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

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