Jordan Structure Of Reflexive Algebras On Banach Space

This thesis is devoted to the investigation of Jordan structure of reflexive algebras onBanach spaces. It consists of four sections. In section 1, we introduce some terminology andnotation, and surnmarize the background and the main contents of this paper. It is provedin section 2 that additive Jordan derivations of certain reflexive algebras are derivations. Inparticular, additive Jordan derivations of nest algebras on Banach spaces are shown to beadditive derivations. In section 3, we show that weakly closed Jordan ideals in nest algebrason Banach spaces are associative ideals. In section 4, we prove that, additive maps preservingzero Jordan products on JSL algebras on Banach spaces are additive Jordan isomorphisms.