JEWELL THEOREM FOR HIGHER DERIVATIONS ON C∗-ALGEBRAS SHIRIN HEJAZIAN MADJID MIRZAVAZIRI and

Let A be an algebra. A sequence {dn} of linear mappings on A is called a higher derivation if dn(ab) = Pn j=0 dj(a)dn−j(b) for each a, b ∈ A and each nonnegative integer n. Jewell [Pacific J. Math. 68 (1977), 91-98], showed that a higher derivation from a Banach algebra onto a semisimple Banach algebra is continuous provided that ker(d0) ⊆ ker(dm), for all m ≥ 1. In this paper, under a different ap-proach using C∗-algebraic tools, we prove that each higher derivation {dn} on a C∗-algebra A is automatically continuous, provided that it is normal, i. e. d0 is the identity mapping on A