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Proceedings of the London Mathematical Society Advance Access published online on August 17, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp026
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© 2009 London Mathematical Society

Multipliers on a new class of Banach algebras, locally compact quantum groups, and topological centres

Zhiguo Hu

Department of Mathematics and Statistics
University of Windsor
Windsor, ON
Canada N9B 3P4

Matthias Neufang

School of Mathematics and Statistics
Carleton University
Ottawa, ON
Canada K1S 5B6
mneufang@math.carleton.ca

Zhong-Jin Ruan

Department of Mathematics
University of Illinois
Urbana, IL 61801
USA
ruan@math.uiuc.edu

Received 30 August 2007. Revision received 22 January 2009.

We study multiplier algebras for a large class of Banach algebras which contains the group algebra L1(G), the Beurling algebras L1(G, {omega}), and the Fourier algebra A(G) of a locally compact group G. This study yields numerous new results and unifies some existing theorems on L1(G) and A(G) through an abstract Banach algebraic approach. Applications are obtained on representations of multipliers over locally compact quantum groups and on topological centre problems. In particular, five open problems in abstract harmonic analysis are solved.

2000 Mathematics Subject Classification 43A10, 43A20, 43A30, 46H05 (primary).

The first and the second authors were partially supported by NSERC. The third author was partially supported by the National Science Foundation DMS-0500535.


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