A bicommutant theorem for dual Banach algebras

Matthew Daws

A bicommutant theorem for dual Banach algebras

Functional Analysis 2010-01-08 v1

Authors: Matthew Daws

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.

Keywords

dual Banach algebra bicommutant theorem reflexive Banach space weak*-continuous homomorphism unital algebra

Cite

@article{arxiv.1001.1146,
  title  = {A bicommutant theorem for dual Banach algebras},
  author = {Matthew Daws},
  journal= {arXiv preprint arXiv:1001.1146},
  year   = {2010}
}

Comments

6 pages

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