Lie Maps And Lie Ideals On Operator Algebras

This thesis is devoted to the investigation of Lie maps and Lie ideals on operator algrbras.It consists of three sections.In Section 1, we introduce some terminology and notation, and summarize the back-ground and the main contents of this paper. In Section 2, we describe the bijective map thatpreserves Lie product on B(X) (the set, of all linear bounded operators on X), and prove thatsuch a map can be written as the sum of two maps, one of which is a ring isomorphism or anegative of a ring anti-isomorphism, and another is a map from B(X) into CI that vanisheson commutators. In Section 3, we show, for a weakly closed linear subspace of a reflexivealgebra with completely distributive and commutative lattice, that it is a Lie ideal if andonly if it is similarity invariant.