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

We study multiplier algebras for a large class of Banach algebras which contains the group algebra L1(G), the Beurling algebras L1(G, ω), 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.