Additive Jordan isomorphisms of nest algebras on normed spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:284

Article

Lu, FY

关键词: Jordan isomorphism;    nest algebra;    nilpotent Jordan ideal;   

DOI  :  10.1016/S0022-247X(03)00287-7

来源: Elsevier

【 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.

【 授权许可】

Free