Jewell theorem for higher derivations on C*-algebras.
Author
Hejazian, Shirin
Mirzavaziri, Madjid
Tehrani, Elahe Omidvar
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/101-10810.4067/S0716-09172010000200003
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.