FW-空间内单位球面上有界线性算子的数值域(英文)  

Numerical ranges of linear bounded operators on the unit sphere of FW-spaces

作　　者：冯孝周[1] 王文锋[2] 米军利[2] 

机构地区：[1]西安工业学院数理系,陕西西安710032 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《宝鸡文理学院学报（自然科学版）》2006年第2期81-84,共4页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

摘　　要：目的研究FW-空间内单位球面上有界线性算子的数值域的几何性质,主要是闭凸性的相关结论。方法引入与FW-空间相关的一个深入定义(即冯-闭凸性)后,给出了FW-空间内单位球面上有界线性算子的数值域必然具有冯-闭凸性的一个不太简短的证明。结果表明了如果H是一个FW-空间,那么它的单位球面上任何有界线性算子的数值域都是一个H的一个冯-闭凸子集。结论作为特殊的Hilbert空间,FW-空间内单位球面上有界线性算子及其数值域有着颇为有趣的性质。Aim Geometric properties of the numerical ranges of linear bounded functionals on the unit sphere of a Banach space over C were investigated, mainly on its Feng-closed convexity. Methods In this note, we make some definitions relative to FW-spaces and an important proposition on Feng- closed convexity. Results This shows that if H is a FW-spaee, then the numerical ranges of linear bounded operators on the unit sphere of H must be a Feng-closed convex set or the intersection of at most countable Feng-closed convex sets in H. Conclusion As a special Hilbert space, the linear bounded functionals on the unit sphere of FW-spaces and their numerical ranges admits fairly interesting properties.

关 键 词：FW-空间 冯-闭凸集 单位球面 闭单位球 H的对偶空间 

分 类 号：O153.3[理学—数学]