Ring Isomorphisms,Complete Preservers And Additive Preservers On Operator Algebras

In this paper,we give some characterization of complete preservers of commutativity,skew commutativity and fixed points of multipliers on ring,obtain new characteristic of ring isomorphism and*-ring isomorphism.Application to several kinds of operators,we get some new results on matrix algebras,Banach algebras,nest algebras,C*-algebras,von Neumann algebras,standard operator algebras Banach spaces,indefinite self-adjoint standard operator algebras on Krein spaces and symmetric standard operator algebras.In addition,a structure result for that preserve rank-1 nilpotent perturbation of scalars on standard operator algebras on Banach space X is discussed.Based on it,a characterization of maps that preserve nilpotent perturbation of scalars in both directions are acquired,and has the form T→cπ(T)+φ(T)I,where c is a scalar,π is a ring isomorphism and φ is a additive functional.