Jordan Maps Of Triangular Banach Algebras

This thesis is devoted to studying Jordan maps of triangular Banach algebras. It consists of four sections.In the first section, we introduce some preliminaries and background. In the second and third sections, it is proved that every bijective mapping preserving Jordan product and/or Jordan triple product of standard subalgebras of nest algebras is additive. In the final section, we give the form of surjective isometric Jordan isomorphisms on triangular Banach algebras, and prove that such isomorphisms are unitarily implemented in some special cases.