‎EXTENSION OF BI-DERIVATIONS TO THE BIDUAL OF A $C^\ast-$ALGEBRA

Azam Erfanian Attar, Sediggeh Barootkoob, Hamid Reza Ebrahimi Vishki

Abstract


‎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 a wide variety of Banach algebras containing $C^*-$algebras‎. ‎In particular‎, ‎we show that the (Arens) extensions of a bi-derivation on $C^*-$algebras are bi-derivations‎. ‎Some results on extensions of an inner bi-derivation are also included‎.

 


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