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We present some necessary and sufficient conditions such that the (Arens) extensions of a bi-derivation on Banach algebras are again bi-derivations. We then examine our results for some Banach algebras. In particular, we show that the (Arens) extensions of a bi-derivation on C∗−algebras are biderivations. Some results on extensions of an inner bi-derivation are also included.

On extension of bi-derivations to the bidual of Banach algebras