Bull. Korean Math. Soc. 2021; 58(5): 1209-1219
Online first article February 24, 2021 Printed September 30, 2021
https://doi.org/10.4134/BKMS.b200873
Copyright © The Korean Mathematical Society.
Lin Chen, Jianhua Zhang
Anshun University; Shaanxi Normal University
Let $G$ be a topological group with a locally compact and Hausdorff topology. Let $\omega$ be a diagonally bounded weight on $G$. In this paper, $(\sigma,\sigma)$-derivation and $(\sigma,\tau)$-weak amenability of the Beurling algebra $L^1_{\omega}(G)$ are studied, where $\sigma,\tau$ are isometric automorphisms of $L^1_{\omega}(G)$. We prove that every continuous $(\sigma,\sigma)$-derivation from $L^1_{\omega}(G)$ into measure algebra $M_{\omega}(G)$ is $(\sigma,\sigma)$-inner and the 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
Supported by: This work is supported by the National Natural Science Foundation of China (No. 12061018) and the Postdoctoral Science Foundation of China (No. 2018M633450). The first author is supported by Foundation of Educational Commission (No. KY[2017]092) and of Science and Technology department (No. [2018]1001) of Guizhou Province of China.
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