delta-DOUBLE DERIVATIONS ON C*-ALGEBRAS

Let A be an algebra and S. E : A --- A be linear mappings.We say that a linear mapping d : A --- A is a (S, E)-doublederivation if d(ab) = d(a)b + ad(b) + 5(a)δ(b) + δ(a)ε(b) for alla, b E A. By a 5-double derivation we mean a (5, 5)-double derivation.Giving some elementary facts concerning double derivations,we prove that if A is a C -algebra, 5 : A -- A is a -linear mappingand d : A -- A is a continuous 5-double derivation tlien 5 iscontinuous. We also show that if A is a C -algebra, 5 : A --- A isa continuous linear mapping and d : A --- A is a .-5-double derivationthen d is continuous, Similar facts concerning (δ. ε)-doublederivations on C*-algebras are also given.