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

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

2006-11-23

arxiv.org/abs/math/0611726v1

Mathematics

Functional Analysis

38 pages

Scientific paper

We study multiplier algebras for a large class of Banach algebras which contains the group algebra $L_1(G)$, the Beurling algebras $L_1(G, \omega)$, and the Fourier algebra $A(G)$ of a locally compact group $G$. This study yields numerous new results and unifies some existing theorems on $L_1(G)$ 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.

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