算子代数上保零积的可加映射(英文)  

Additive Maps Preserving Zero-product on Operator Algebras

作　　者：赵连阔[1] 侯晋川[1] 

机构地区：[1]山西师范大学数学与计算机科学学院,山西临汾041004

出　　处：《山西师范大学学报（自然科学版）》2004年第4期21-25,共5页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目资助(编号:10071046);山西省自然科学基金项目资助(编号:20021005).

摘　　要：本文分别刻画了Hilbert空间上自伴算子空间和对称算子空间上双边保零积的可加满射,Hilbert空间上包含单位元和所有有限秩算子的 子代数上双边保半正交性的可加满射,以及vonNeumann代数上,C 代数上和Banach空间标准算子代数上保约当零积的可加或线性满射.In this paper we give some characterizations of the surjective additive maps on the space of self-product in both directions, the surjective additive maps on the unital *-subalgebras containing all finite rank operators which preserve semi-orthogonality in both directions as well as the surjective additive (or linear) maps on the unital *-subalgebras containing all finite rank operators which preserve semi-orthogonality in both directions as well as the surjective additive (or linerar) maps on such operator algebras as von Neumann algebras, C~*-algebras and standard operator algebras which preserve Jordan zero-product.

关 键 词：算子代数 满射 Hilbert空间 VONNEUMANN代数 单位元 C^＊代数 半正 上包 标准 对称 

分 类 号：N02[自然科学总论—科学技术哲学] O177[理学—数学]