Jordan On The Cover Depicts Isomorphic Algebra

In this paper, we mainly discuss linear maps preserving Jordan products and ξ-Lie products on the set determined by zero products of nest algebras, the details as following:In Chapter1, some notations, definitions (for example, nest algebras, isomor-phism, anti-isomorphism, Jordan isomorphism and so on) are given.In Chapter2, we characterize the Jordan isomorphism between nest algebras on separable complex Hilbert space, and prove that every linear unital bijection preserving Jordan products on the set determined by zero products of nest algebras is either an isomorphism or an anti-isomorphism.In Chapter3, we study unital bijections preserving ξ-Lie products on the set determined by zero products of nest algebras, and show that such a map is either an isomorphism or an anti-isomorphism.