Additive Jordan isomorphisms of nest algebras on normed spaces

摘要

Let X be a real or complex Banach space. Let algN and algM be two nest algebras on X. Suppose that phi is an additive bijective mapping from algN onto algM such that phi(A(2)) = phi(A)(2) for every A is an element of algN. Then phi is either a ring isomorphism or a ring anti-isomorphism. Moreover, if X is a real space or an infinite dimensional complex space, then there exists a continuous (conjugate) linear bijective mapping T such that either phi(A) = TAT(-1) for every A is an element of algN or theta(A) = TA * T-1 for every A is an element of algN. (C) 2003 Published by Elsevier Inc. [References: 13]