Mathematics > Functional Analysis
[Submitted on 18 Jan 2022 (v1), last revised 21 Jan 2022 (this version, v2)]
Title:On the algebraic structures in $\A_Φ(G)$
View PDFAbstract:Let $G$ be a locally compact group and $(\Phi, \Psi)$ be a complementary pair of $N$-functions. In this paper, using the powerful tool of porosity, it is proved that when $G$ is an amenable group, then the Figà-Talamanca-Herz-Orlicz algebra ${\A}_{\Phi}(G)$ is a Banach algebra under convolution product if and only if $G$ is compact. Then it is shown that ${\A}_{\Phi}(G)$ is a Segal algebra, and as a consequence, the amenability of ${\A}_{\Phi}(G)$ and the existence of a bounded approximate identity for ${\A}_{\Phi}(G)$ under the convolution product is discussed. Furthermore, it is shown that for a compact abelian group $G$, the character space of ${\A}_{\Phi}(G)$ under convolution product can be identified with $\widehat{G}$, the dual of $G$.
Submission history
From: Hamid Rahkooy [view email][v1] Tue, 18 Jan 2022 11:57:29 UTC (11 KB)
[v2] Fri, 21 Jan 2022 17:43:39 UTC (11 KB)
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