Characterizations Of A Pair Of Generalized Derivations On Triangular Algebras

In this paper, we mainly study a pair of generalized derivable linear mappings at zero point on nest algebras and a pair of generalized derivable linear mappings at unit point on triangular algebras. The details are as follows:In Chapter1, we give some common symbols, definitions (for example, nest algebras, triangular algebras, generalized derivation, a pair of generalized derivation) and so on.In Chapter2, we characterize a pair of generalized derivable linear mappings at zero point between nest algebras on separable complex Hilbert space, and prove that a pair of generalized derivable linear mappings at zero point on nest algebras is a pair of generalized derivations.In Chapter3, we study a pair of generalized derivable linear mappings at unit point on triangular algebras, and show that a pair of generalized derivable linear mappings at unit point on triangular algebras is a pair of generalized derivations.