BSE-property for some certain Segal and Banach algebras

Mohammad Fozouni

Published 2016-04-06Version 1

We study the BSE-property of some certain Segal algebras which introduced recently by J. Inoue and S.-E. Takahasi and as an application, we provide examples of Banach algebras without any bounded weak approximate identity. If $G$ is a locally compact group, for a measurable and sub-multiplicative function $\tau:G\longrightarrow \mathbb{C}^{\times}$, we define the Banach algebra $L^{1}(G)_{\tau(n)}$ consisting of all $f\in L^{1}(G)$ with $f\tau, f\tau^{2},..., f\tau^{n}\in L^{1}(G)$ and norm $\|f\|_{\tau(n)}=\sum_{k=0}^{n}\|f\tau^{k}\|_{1}$, then we investigate the BSE-property of this new Banach algebra.