Some Problems On The Local Mappings For Nonselfadjoint Operator Algebras

This thesis concerns the problems on the local mappings and the linear mappings presevering idempotents for some non-selfadjoint operator algebras. It consists of two chapters.In chapter 1, we study the the linear mapping satisfying the property of the derviation operatoration on every idempotent in a digraph algebra, and show that such a mappings is a derivation, which generalizes the results on the local derivation of digraph algebras.In chapter 2, we study the linear mappings presvering idempotents of the finite dimensional CSL algebras and the linear surjective 2-local isometric antiautomorphism on the completely distributive commutative subspace lattice algebras, and show that the linear mappings presvering idempotents are Jordan homomorphisms and such a 2-local isometric antiautomorphism is also a an antiautomorphism.