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Research Article | Open Access

On generalized biderivations of Banach algebras

Department of Mathematics, Aydın Adnan Menderes University, Aydın, Turkey
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Abstract

The aim of this paper is to introduce the concept of generalized biderivations of unital Banach algebras and prove some results concerning generalized biamenability of unital Banach algebras. Let A and B be unital Banach algebras, and let X be a unital A- B-module. Let T=Tri(A,X,B) be the corresponding triangular Banach algebra. We also study the generalized biamenability of triangular Banach algebras and show that if X={0} and T is generalized biamenable, then A and B are both generalized biamenable.

Keywords

generalized biderivationinner generalized biderivationgeneralized biamenabilityweak generalized biamenabilitytriangular Banach algebra
CLC number: 15A78, 46H25

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 36259-36272
DOI: 10.3934/math.20241720

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Arslan B. On generalized biderivations of Banach algebras. AIMS Mathematics, 2024, 9(12): 36259-36272. https://doi.org/10.3934/math.20241720

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Received: 15 October 2024
Revised: 11 December 2024
Accepted: 20 December 2024
Published: 15 December 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)