International Journal of Nonlinear Analysis and Applications

Idempotent multipliers of Figa-Talamanca-Herz algebras

Document Type : Research Paper

Authors

1 Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran

2 Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Abstract

For a locally compact group $G$ and $p\in(1,\infty)$, let $B_p(G)$ is the multiplier algebra of the Fig\`{a}-Talamanca-Herz algebra $A_p(G)$. For $p=2$ and $G$ amenable, the algebra $B(G):= B_2(G)$ is the usual Fourier-Stieltjes algebra. In this paper, we show that $A_p(G)$ is a Bochner-Schoenberg-Eberlin (BSE) algebra and every clopen subset of $G$ is a synthetic set for $A_p(G)$. Furthermore, we characterize idempotent elements of the Banach algebra $B_p(G)$. This result generalizes the Cohen-Host idempotent theorems for the case of Fig\`{a}-Talamanca-Herz algebras. Characterization of idempotent elements of $B_p(G)$ is of paramount importance to study homomorphisms in Fig\`{a}-Talamanca-Herz algebras.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 1
January 2025
Pages 371-376
  • Receive Date: 05 September 2022
  • Revise Date: 30 December 2023
  • Accept Date: 30 December 2023