Local Mappings On Operator Algebras

This thesis is devoted to the investigation of local mappings of operator algebras. 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. It is proved in section 2 that every 2-local automorphism of a symmetric finite dimensional commutative subspace lattice algebra is an automorphism. For the non-symmetric case, we produce an counter-example which negatively answers the Crist's conjecture. In section 3, we show that a local derivation is a darivation on a standard subalgebra of a J-subspace lattice algebra which contains the identity. Finally, the additivity of multiplicative mappings is studied in section 4. We first, extend the famous Mart.indale's theorem to the ring which need not contain iderr potents. Applying this result, we show that every multiplicative mapping is additive, from the Jacobson radical of a nest algebra associated to the nest whose extreme poinls are continuous, onto any ring.