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∈(1,∞), let Bp(G) is the multiplier algebra of the Fig\`{a}-Talamanca-Herz algebra Ap(G). For p=2 and G amenable, the algebra B(G):=B2(G) is the usual Fourier-Stieltjes algebra. In this paper, we show that Ap(G) is a Bochner-Schoenberg-Eberlin (BSE) algebra and every clopen subset of G is a synthetic set for Ap(G). Furthermore, we characterize idempotent elements of the Banach algebra Bp(G). This result generalizes the Cohen-Host idempotent theorems for the case of Fig\`{a}-Talamanca-Herz algebras. Characterization of idempotent elements of Bp(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