Additive maps preserving Jordan zero-products on nest algebras

作者：Hou Jinchuan^*; Jiao Meiyan

来源：Linear Algebra and Its Applications, 2008, 429(1): 190-208.

DOI：10.1016/j.laa.2008.02.021

• Banach space operators
• nest algebras
• Jordan zero-products
• Jordan isomorphisms

Let AlgN and AlgM be nest algebras associated with the nests N and M on Banach Spaces. Assume that N is an element of N and M is an element of M are complemented whenever N_ = N and M_ = M. Let Phi: AlgN -> AlgM be a unital additive surjection. It is shown that Phi preserves Jordan zero-products in both directions, that is Phi(A)Phi(B) + Phi(B)Phi(A) = 0 double left right arrow AB + BA = 0, if and only if Phi is either a ring isomorphism or a ring anti-isomorphism. Particularly, all unital additive surjective maps between Hilbert space nest algebras which preserves Jordan zero-products are characterized completely.

• 出版日期2008-7-1
• 单位山西农业大学