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Following Villena in [9] and Mohammed and Ali in [4], we introduce partially defined ( ) c double derivation and generalized ( ) c double derivation on a semisimple complex Banach algebra whose domain is not necessarily closed, essential ideal and we prove that they are closable. In particular, we show that every ( )c -double derivation and generalized ( ) c double derivation defined on any nonzero ideal of a prime C * algebra are continuous.

Automatic Continuity of Some Types of Double Derivations on Semisimple Banach Algebras