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.
Citation: Berna Arslan. On generalized biderivations of Banach algebras[J]. AIMS Mathematics, 2024, 9(12): 36259-36272. doi: 10.3934/math.20241720
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.
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Berna Arslan. On generalized biderivations of Banach algebras[J]. AIMS Mathematics, 2024, 9(12): 36259-36272. doi: 10.3934/math.20241720
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