Characterization Of Jordan Higher Derivations And Derivations On Operator Algebras

Jordan higher derivable maps and derivations as two classes are very important in the mathematical theory of mapping, and received extensive attention of numerous mathematical researchers. In this article we will make further discussion and research on its.The structure of this paper as follows:In the first chapter, we introduce the background of the discussed problem of this thesis briefly, the main work of this article, and the several notation used in the article.In the second chapter, we show that every Jordan higher derivable map on an irreducible CDCSL algebra or a nest algebra is a higher derivation, and new charac-terizations of higher derivations on these algebras are obtained.In the third chapter, we give a necessary and sufficient condition for an additive map5:Râ†'M to be derivable at β with β=pβ=βp. In particular, we show that an additive map δ:B(X)â†'B(X) is derivable at any nonzero finite rank operator if and only if it is a derivation.