Abstract
Let $A$ and $B$ be unital Banach algebrasâ, â$X$ be an unital $A-B-$module and $T$ be the triangular Banach algebra associated to $Aâ, âB$ and $X$â. The structure of some derivations on triangular Banach algebras was studied by some authors. ââNote that despite the apparent similarity between derivations and biderivations and also inner derivations and inner biderivationsâ, âthere are fundamental differences between themâ. Although there are some studying of biderivations on triangular Banach algebras, any of them do not completely determine the structure of biderivations on triangular Banach algebras. In this paper, we âcompletely characterize biderivations and inner biderivations from $T\times T$ to $T^*$â and we show that the first bicohomology group $BH^1(T, T^*)$ is equal to $BH^1(A, A^*)\oplus BH^1(B, B^*)$ââ.
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