The Structure Of Lie Derivations On Reflexive Operator Algebras

This thesis is devoted to the investigation of the structure of Lie derivations on reflexive operator algebras on Banach spaces.It consists of four sections.In section 1,we introduce some terminology and notation,and summarize the background and the main contents of this paper.In section 2,we study the structure of Lie derivations on reflexive operator algebras whose invariant lattices have the non-trivial greastest or smallest elements.In section 3,we study the structure of Lie derivations on nest algebras on Banach spaces.In section 4,we study the structure of Lie derivable maps.