Daws, M (2010) Multipliers of locally compact quantum groups via Hilbert C*-modules. Journal of the London Mathematical Society, 84 (2). 385 - 407 (23). ISSN 0024-6107
Abstract
A result of Gilbert shows that every completely bounded multiplier $f$ of the Fourier algebra $A(G)$ arises from a pair of bounded continuous maps $\alpha,\beta:G \rightarrow K$, where $K$ is a Hilbert space, and $f(s^{-1}t) = (\beta(t)|\alpha(s))$ for all $s,t\in G$. We recast this in terms of adjointable operators acting between certain Hilbert C$^*$-modules, and show that an analogous construction works for completely bounded left multipliers of a locally compact quantum group. We find various ways to deal with right multipliers: one of these involves looking at the opposite quantum group, and this leads to a proof that the (unbounded) antipode acts on the space of completely bounded multipliers, in a way which interacts naturally with our representation result. The dual of the universal quantum group (in the sense of Kustermans) can be identified with a subalgebra of the completely bounded multipliers, and we show how this fits into our framework. Finally, this motivates a certain way to deal with two-sided multipliers.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2010, London Mathematical Society. This is an author produced version of a paper published in the Journal of the London Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy |
Dates: |
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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 12:23 |
Last Modified: | 29 Mar 2018 05:44 |
Published Version: | http://dx.doi.org/10.1112/jlms/jdr013 |
Status: | Published |
Publisher: | London Mathematical Society |
Identification Number: | 10.1112/jlms/jdr013 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77174 |