Effects On Operator Algebras

This thesis mainly study the maps on effect algebras E(H)of Hilbert space H and effect algebras E(A)of some C~*-algebras,concerning local map,two local map,morphism and so on.This thesis consists of three chapters.In chapter one,we characterize one surjective two local sequential automorphism and two local E-antomorphism on effect algebras E(H).Rely on characterizing the projections on the Hilbert space H,when dimension of H is equal to or more than three,we prove that each surjective two local sequential automorphism on effect algebras E(H)has the formφ(A)=UAU~*,where U is unitary or anti-unitary operator.We prove that each surjective two local E-automorphism on effect algebras E(H)is E-automorphism,therefore,we get each surjective and linear two local E-automorphism on real space B_s(H)is not only a Jordan automorphism but also has the formφ(A)=UAU~*,where U is unitary or antiunitary operator.In addition,for the effect algebra E(A)of factor von Neumann algebra A,we prove that each E-automorphism on effect algebras E(A)can be extended to a*automorphism or *-anti-automorphism on the whole factor algebras.In chapter two,we study the structure and extension of morphism and homomorphism on effect algebras E(H)and E(A).when dimension of H is equal to or more than three,we prove that each surjective and strongσ-ortheomplete homomorphism has the formφ(A)=UAU~*,where U is unitary or anti unitary operator;we also prove that homomorphism from E(A)into E(H)satisfy homogeneity and preserve order in one side can be extended to a bounded Jordan *-homomorphism from von Neumann algebra A into B(H),especially,when A is commutative von Neumann algebra,the homomorphism can be extended to a bounded *-homomorphism from von Neumann algebra A into algebraIn chapter three,we study sequential automorphism and automorphism on effect algebras E(A)of C~*-standard operator algebra,We generalize some related results on effect algebras E(H)of Molnar,but the method is different from Molnar's.Rely on characterizing the finite rank projections on the Hilbert space H which dimension is equal to or more than three,we prove that both sequential automorphism and automorphism on effect algebras E(A)have the formsφ(A)=UAU~*,where U is unitary or anti unitary operator.We also prove that the bijective map on effect algebras A under the conditions of preserving Jordan product has the formφ(A)=UAU~*,where U is unitary or anti unitary operator.