Jewell theorem for higher derivations on C*-algebras.

• Hejazian, Shirin ^[1] ; Mirzavaziri, Madjid ^[1] ; Tehrani, Elahe Omidvar ^[1]
  1. [1] Ferdowsi University of Mashhad

     Ferdowsi University of Mashhad

     Irán

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 29, Nº. 2, 2010, págs. 101-108
• Idioma: inglés
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• Resumen

  • 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.