Document Type : Original Paper

Authors

• H. Mahdavian Rad
• A. Niknam

Department of Mathematics, Faculty of Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran

Abstract

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some theorems and corollaries about the automatic continuity of this notion.

Keywords

• Derivation
• ( )-Derivation
• -Double derivation
• Higher double derivation