الملخص

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.