A bicommutant theorem for dual Banach algebras

Details A bicommutant theorem for dual Banach algebras A bicommutant theorem for dual Banach algebras

2010-01-07

arxiv.org/abs/1001.1146v1

Mathematics

Functional Analysis

6 pages

Scientific paper

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.

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