A bicommutant theorem for dual Banach algebras
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2010
- DOI:
- 10.48550/arXiv.1001.1146
- arXiv:
- arXiv:1001.1146
- Bibcode:
- 2010arXiv1001.1146D
- Keywords:
-
- Mathematics - Functional Analysis;
- 46H05;
- 46H15;
- 47L10
- E-Print:
- 6 pages