保算子乘积数值域的映射(英文)  

Maps Preserving Numerical Range of Products of Operators

作　　者：狄青会[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）》2005年第1期1-4,共4页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10071046);山西省自然科学基金资助项目(20021005)

摘　　要：算子数值域是一个非常重要的概念,它在理论和应用方面都得到了广泛的研究.在保持问题的研究方面,人们已经在不同的算子代数上做了许多刻画保数值域映射的工作。本文主要在某些算子代数或算子空间上研究保算子乘积数值域的映射的刻画问题。我们得到β(Hi)或Sa (Hi) (i=1, 2)之间保算子乘积数值域的映射的刻画、保算子斜乘积数值域的映射的刻画、保Jordan三重积数值域的映射的刻画以及保Jordan斜三重积数值域的映射的刻画.我们的结果表明上述映射具有良好的结构且在许多情形给出了* 同构或* 反同构的新特征.Numerical range of operators is a very important concept and it is extensively studied both in theory and applications. Concerning with the preserver problems, a lot of work have been done on maps preserving numerical range on various operator algebras. In this paper we mainly study the maps between some operator algebras of operator spaces which preserve numerical range of products of operators. Let H_i be complex Hibert spaces, i=1,2. For each i, let (B(H_i)) be the algebra of all bounded linear operators acting on H_i and (S ~a(H_i) )the real linear subspace of all self-adjoint operators in (B(H_i)). We characterize the surjective maps between B(H_i) or S ~a(H_i), i=1,2, which preserve the numerical range of products of operators, or of skew products of operators, or of Jordan triple-products of operators, or of skew products of operators, or of Jordan triple-products of operators, or of Jordan skew triple-products of operators. Such maps are thoronghly classified, and it turns out, they have very nice structures. In many cases, our results give new characterizations of *-isomorphisms and *-anti-isomorphisms.

关 键 词：数值域 刻画 乘积 算子代数 映射 算子空间 同构 概念 保持 理论 

分 类 号：N941[自然科学总论—系统科学] O177[理学—数学]