On generalized biderivations of Banach algebras

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 biderivation
• inner generalized biderivation
• generalized biamenability
• weak generalized biamenability
• triangular banach algebra