The Additivity Of Elementary Maps On Symmetric Operator Spaces

The research of operator algebra has attracted many scholars'attention, pre-serving problem in operator algebras is also an active research topic. With the definitions of elementary maps, Jordan elementary maps and Jordan-triple elemen-tary maps are given, many scholar discussed these maps and obtained tremendous achievements in operator algebra. This paper also has something to do with these maps. Firstly, we discuss Jordan elementary maps on symmetric operator spaces. Secondly, we research Jordan-triple elementary maps on symmetric operator spaces.This paper contains three chapters:In Chapter 1, we introduce some definitions which will be used in this paper. Firstly, this paper gives some notations. Secondly, the definitions of adjoint operator, symmetric operator, Jordan elementary maps and Jordan-triple elementary maps are given.In Chapter 2. we mainly discuss Jordan elementary maps. The additivity of these maps on symmetric operator spaces are proved.In Chapter 3. we research elementary maps which is more extensive. We prove the additivity of Jordan-triple elementary maps on symmetric operator spaces, which is an extend of Chapter 2.