TY - JOUR ID - 32083 TI - Double Derivations, Higher Double Derivations and Automatic Continuity JO - Journal of Sciences, Islamic Republic of Iran JA - JSCIENCES LA - en SN - 1016-1104 AU - Mahdavian Rad, H. AU - Niknam, A. AD - Department of Mathematics, Faculty of Mathematics, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran Y1 - 2013 PY - 2013 VL - 24 IS - 2 SP - 165 EP - 170 KW - Derivation KW - ( )-Derivation KW - -Double derivation KW - Higher double derivation DO - N2 - 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. UR - https://jsciences.ut.ac.ir/article_32083.html L1 - https://jsciences.ut.ac.ir/article_32083_a3fea6fd0fece698a82950d6b3210a49.pdf ER -