JEWELL THEOREM FOR HIGHER DERIVATIONS ON C*-ALGEBRAS

Abstract

Let A be an algebra. A sequence {dn} of linear mappings on A is called a higher derivation if 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 approach 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.