A bicommutant theorem for dual Banach algebras

2010/01/07 by Matthew Daws, Daws, Matthew
Mathematics · #46H05 #46H15 #47L10 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46H05 #msc:46H15 #msc:47L10

paper · pdf · doi:10.48550/arxiv.1001.1146

6 pages

arxiv created 2010/01/07 · arxiv updated 2010/01/14

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→\mc B(E) such that π(\mc A) equals its own bicommutant.

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