Lie Maps On Operator Algebras

This thesis is devoted to the investigation of maps preservingξ-Lie product on nest algebras and centeralizers on standard subalgebras.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 give a strutural theorem of maps preserving Lie product on nest algebras.In section 3,we prove the additivity of maps preservingξ-Lie product on nest algebras.In section 4,we characterize centralizers on standard subalgebras.