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

Abstract

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.

38 pages

References in corpus (1)

• Locally Compact Quantum Groups. A von Neumann Algebra Approach

Cited by in corpus (9)

• Completely positive definite functions and Bochner's theorem for locally compact quantum groups
• Module homomorphisms and multipliers on locally compact quantum groups
• Generalized fixed point algebras for coactions of locally compact quantum groups
• Poisson boundaries over locally compact quantum groups
• Multipliers over Fourier algebras of ultraspherical hypergroups
• Duality, Cohomology, and Geometry of Locally Compact Quantum Groups
• Quantum information theory and Fourier multipliers on quantum groups
• Geometry of $C^{\ast }$-algebras, the bidual of their projective tensor product, and completely bounded module maps
• Fourier spaces and completely isometric representations of Arens product algebras