Additivity Of Jordan Elementary Maps

This thesis mainly study the additivity of maps on standard Jordan operator algebras and triangular algebras,concerning Jordan elementary map and Jordan triple elementary map.This thesis consists of two chapters.In chapter one,We study the additivity of Jordan elementary maps on standard Jordan operator algebras.We prove that Jordan elementary surjective maps on standard Jordan operator algebras on a Hilbert space of dimension＞1 are automatically additive by making use of purely algebraic method.In chapter two,We study the additivity of Jordan triple elementary maps on triangular algebras,a special non-self-adjoint algebra.Relying on the matrix structure of triangular algebra and purely algebraic method called Pierce decomposition, we show that Jordan triple elementary surjective maps on triangular algebras which satisfy certain conditions are additive.