# Multipliers of multidimensional Fourier algebras

Ivan Todorov, L. Turowska

Research output: Contribution to journalArticlepeer-review

## Abstract

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.
Original language English 459-484 26 Operators and Matrices 4 4 Published - 2010

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• ### R1736PMR: Operator Multipliers

Todorov, I.

01/08/2005 → …

Project: Research