Daws, M (2010) Multipliers, self-induced and dual Banach algebras. Dissertationes Mathematicae (470). 5 - 59 (54). ISSN 0012-3862
Abstract
In the first part of the paper, we present a short survey of the theory of multipliers, or double centralisers, of Banach algebras and completely contractive Banach algebras. Our approach is very algebraic: this is a deliberate attempt to separate essentially algebraic arguments from topological arguments. We concentrate upon the problem of how to extend module actions, and homomorphisms, from algebras to multiplier algebras. We then consider the special cases when we have a bounded approximate identity, and when our algebra is self-induced. In the second part of the paper, we mainly concentrate upon dual Banach algebras. We provide a simple criterion for when a multiplier algebra is a dual Banach algebra. This is applied to show that the multiplier algebra of the convolution algebra of a locally compact quantum group is always a dual Banach algebra. We also study this problem within the framework of abstract Pontryagin duality, and show that we construct the same weak* topology. We explore the notion of a Hopf convolution algebra, and show that in many cases, the use of the extended Haagerup tensor product can be replaced by a multiplier algebra.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Keywords: | multiplier; double centraliser; Fourier algebra; locally compact quantum group; dual Banach algebra; Hopf convolution algebra |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Dec 2013 12:41 |
Last Modified: | 15 Sep 2014 02:36 |
Published Version: | http://dx.doi.org/10.4064/dm470-0-1 |
Status: | Published |
Publisher: | Polish Academy of Sciences |
Identification Number: | 10.4064/dm470-0-1 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77175 |