Mathematica Bohemica, Vol. 144, No. 1, pp. 1-11, 2019


Generalization of the weak amenability on various Banach algebras

Madjid Eshaghi Gordji, Ali Jabbari, Abasalt Bodaghi

Received May 14, 2017.   First published March 26, 2018.

Abstract:  The generalized notion of weak amenability, namely $(\varphi,\psi)$-weak amenability, where $\varphi,\psi$ are continuous homomorphisms on a Banach algebra ${\mathcal A}$, was introduced by Bodaghi, Eshaghi Gordji and Medghalchi (2009). In this paper, the $(\varphi,\psi)$-weak amenability on the measure algebra $M(G)$, the group algebra $L^1(G)$ and the Segal algebra $S^1(G)$, where $G$ is a locally compact group, are studied. As a typical example, the $(\varphi,\psi)$-weak amenability of a special semigroup algebra is shown as well.
Keywords:  Banach algebra; $(\varphi,\psi)$-derivation; group algebra; locally compact group; measure algebra; Segal algebra; weak amenability
Classification MSC:  46H20, 43A20


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Affiliations:   Madjid Eshaghi Gordji, Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran, and Center of Excellence in Nonlinear Analysis and Applications (CENAA), Semnan University, Iran, e-mail: madjid.eshaghi@gmail.com; Ali Jabbari, Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran e-mail: jabbari_al@yahoo.com; Abasalt Bodaghi (corresponding author), Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran, e-mail: abasalt.bodaghi@gmail.com


 
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