任意Banach空间中线性算子的Moore-Penrose度量广义逆

倪仁兴;

数学学报 ›› 2006, Vol. 49 ›› Issue (6) : 1247-125.

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数学学报 ›› 2006, Vol. 49 ›› Issue (6) : 1247-125. DOI: 10.12386/A2006sxxb0156
论文

任意Banach空间中线性算子的Moore-Penrose度量广义逆

    倪仁兴;
作者信息 +

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

    Ren Xing NI
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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.

Abstract

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

Moore-Penrose度量广义逆 / 线性算子 / 广义正交分解

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倪仁兴;. 任意Banach空间中线性算子的Moore-Penrose度量广义逆. 数学学报, 2006, 49(6): 1247-125 https://doi.org/10.12386/A2006sxxb0156
Ren Xing NI. Moore-Penrose Metric Generalized Inverse of Linear Opeartor in Arbitrary Banach Space. Acta Mathematica Sinica, Chinese Series, 2006, 49(6): 1247-125 https://doi.org/10.12386/A2006sxxb0156
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