B(H)上保因子交换性可加映射的刻画  

Characterization of Additive Maps Preserving Commutativity up to a Factor on B(H)

作　　者：焦美艳[1] 侯晋川[2] 

机构地区：[1]山西大学数学科学学院,山西太原030006 [2]太原理工大学数学系,山西太原030024

出　　处：《中北大学学报（自然科学版）》2008年第3期206-209,共4页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10771157)

摘　　要：算子的因子交换性是算子代数之间同构的不变量之一.进一步研究其逆命题是否成立的问题,有助于加深因子交换性与算子代数的代数和几何性质之间相互制约关系的理解.利用算子理论和方程的技巧,在没有保单位的假设条件下,证明了无限维希尔伯特空间算子代数之间保持因子交换性的可加满射是同构,或(在某些情形)共轭同构或共轭反同构的常数倍.Commutativity up to a factor is one of the invariants of isomophisms among operator algebras. The study of the question that whether the converse proposition holds true is helpful to understand the relations between commutativity up to a factor and the algebraic as well as the geometric properties of operator algebras. By using some techniques in operator theory, without the assumption that maps are unit-preserving, it is shown that every subjective additive map among the whole infinite dimensional Hilbert operator algebras that preserves commutativity up to a factor is a scalar multiple of an isomorphism, or （in some situations） a conjugate isomorphism or a conjugate anti isomorphism.

关 键 词：HILBERT空间 因子交换性 JORDAN同构 

分 类 号：O177.1[理学—数学]