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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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[1] P.J. Cohen, Homomorphisms and idempotents of group algebras, Bull. Amer. Math. Soc. 65 (1959), 120–122. [2] P.J. Cohen, On a conjecture of Littlewood and idempotent measures, Amer. J. Math. 82 (1960), 191–212. [3] P. Eymard, L’algebre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236. [4] B. Forrest, Amenability and bounded approximate identities in ideals of A(G), Illinois J. Math. 34 (1990), 1–25. [5] C.S. Herz, The theory of p-spaces with an application to convolution operators, Trans. Amer. Math. Soc. 154 (1971), 69–82. [6] C.S. Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier 23 (1973), 91–123. [7] B. Host, Le theoreme des idempotents dans B(G), Bull. Soc. Math. France 114 (1986), 215–223. [8] M. Ilie, On Fourier algebra homomorphisms, J. Funct. Anal. 213 (2004), 88–110. [9] M. Ilie, Completely bounded homomorphisms of the Fourier algebras, J. Funct. Anal. 225 (2005), 480–499. [10] R. Larsen, An Introduction to the Theory of Multipliers, Springer, Berlin, 1971. [11] R. Larsen, Banach Algebra: An Introduction, Dekker, New York, 1973. [12] J.-P. Pier, Amenable Locally Compact Groups, John Wiley & Sons Inc., New York, 1984. [13] S.-E. Takahasi and O. Hatori, Commutative Banach algebras which satisfy a Bochner-Schoenberg-Eberlein type-theorem, Proc. Amer. Math. Soc. 110 (1990), no. 1, 149–158. [14] A. Ulger, Multipliers with closed range on commutative semisimple Banach algebras, Studia Math. 153 (2002), 59–80. | ||
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