Characterization of ۲-cocycles and ۲-coboundaries on Direct Sum of Banach Algebras

Let A and B be Banach algebras. In this paper, we investigate the structure of ۲-cocycles and ۲-coboundaries on A\oplus B, when  A and B are unital.  Actually, we provide a specific criterion for each ۲-cocycle map and establish a connection between ۲-cocycles and ۲-coboundaries on A\oplus B and ۲-cocycles and ۲-coboundaries on A and B. Finally, our results lead to a connection between  \mathcal{H}^۲(A, A^{*}), \mathcal{H}^۲(B, B^{*}) and \mathcal{H}^۲(A\oplus B, A^{*}\oplus B^{*}).

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