- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 $(\sigma, \sigma)$-derivation and $(\sigma, \tau)$-weak amenability of Beurling algebra Bull. Korean Math. Soc.Published online February 24, 2021 Lin Chen and Jianhua Zhang Shannxi Normal University Abstract : Let $G$ be a topological group with a locally compact and Hausdorff topology. $\omega$ is a diagonally bounded weight. In this paper, the generalized notions of derivation and weak amenability, namely $(\sigma,\tau)$-derivation and $(\sigma,\tau)$-weak amenability, where $\sigma,\tau$ are isometric automorphism of Banach algebra, are studied on Beurling algebra $L^1_{\omega}(G)$. We prove that every continuous $(\sigma,\sigma)$-derivation from $L^1_{\omega}(G)$ into measure algebra $M_{\omega}(G)$ is $(\sigma,\sigma)$-inner and Beurling algebra $L^1_{\omega}(G)$ is $(\sigma,\tau)$-weakly amenable. Keywords : $(\sigma,\sigma)$-derivation; $(\sigma,\tau)$-weak amenability; Beurling algebras MSC numbers : 47B49; 46K15 Full-Text :