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Idempotent multipliers of Figa-Talamanca-Herz algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 30، دوره 16، شماره 1، فروردین 2025، صفحه 371-376 اصل مقاله (389.62 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28296.3854 | ||
| نویسندگان | ||
| Ahmad Karimi1؛ Choonkil Park* 2 | ||
| 1Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran | ||
| 2Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea | ||
| تاریخ دریافت: 14 شهریور 1401، تاریخ بازنگری: 09 دی 1402، تاریخ پذیرش: 09 دی 1402 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Figa-Talamanca-Herz algebra؛ Multiplier algebra؛ Idempotent element؛ Fourier algebra؛ Fourier-Stieltjes algebra | ||
| مراجع | ||
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