University of TehranJournal of Sciences, Islamic Republic of Iran1016-110424220130601Double Derivations, Higher Double Derivations
and Automatic Continuity16517032083ENH.Mahdavian RadDepartment of Mathematics, Faculty of Mathematics, Ferdowsi University of
Mashhad, Mashhad, Islamic Republic of IranA.NiknamDepartment of Mathematics, Faculty of Mathematics, Ferdowsi University of
Mashhad, Mashhad, Islamic Republic of IranJournal Article20121010Let 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.https://jsciences.ut.ac.ir/article_32083_a3fea6fd0fece698a82950d6b3210a49.pdf