任意Banach空间中线性算子的Moore-Penrose度量广义逆  

Moore-Penrose Metric Generalized Inverse of Linear Opeartor in Arbitrary Banach Space

作　　者：倪仁兴[1] 

机构地区：[1]绍兴文理学院数学系,浙江绍兴312000

出　　处：《数学学报（中文版）》2006年第6期1247-1252,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(10271025);浙江省自然科学基金(102002)

摘　　要：在无空间严格凸的几何假定下,利用Banach空间几何方法给出了任意Banach空间中线性算子T的Moore-Penrose度量广义逆T^+的存在性、唯一性、极小性和线性性的充要条件,同时还讨论了T^+的一些性质,这些本质地将文献[8]的最近结果从严格凸Banach空间拓广至任意Banach空间．Without geometry assumption on strictly convex space, by means of methods of geometry of Banach space, the necessary and sufficient conditions for the existence, uniqueness, minimum property and linearity of the Moore-Penrose metric generalized inverse T^＋ of linear operator T are given, and some properties of T^＋ are investigated. These indeed extend and improve the corresponding recent results obtained by [8] from strictly convex Banach space to arbitrary Banach space.

关 键 词：线性算子 Moore-Pcnrose度量广义逆 广义正交分解 

分 类 号：O177.2[理学—数学]