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首页> 外文期刊>Journal of Mathematical Analysis and Applications >Metric generalized inverse for linear manifolds and extremal solutions of linear inclusion in Banach spaces
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Metric generalized inverse for linear manifolds and extremal solutions of linear inclusion in Banach spaces

机译：Banach空间中线性流形的度量广义逆和线性包含的极值解

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摘要

Let X, Y be Banach spaces and M a linear manifold in X x Y = {{x, y} x is an element of X, y is an element of Y}. The central problem which motivates many of the concepts and results of this paper is the problem of characterization and construction of all extremal solutions of a linear inclusion y is an element of M(x). First of all, concept of metric operator parts and metric generalized inverses for linear manifolds are introduced and investigated, and then, characterizations of the set of all extremal or least extremal solutions in terms of metric operator parts and metric generalized inverses of linear manifolds are given by the methods of geometry of Banach spaces. The principal tool in this paper is the generalized orthogonal decomposition theorem in Banach spaces. (C) 2004 Published by Elsevier Inc.
机译：令X，Y为Banach空间，M为X的线性流形x Y = {{x，y} x为X的元素，y为Y}的元素。激发本文许多概念和结果的核心问题是特征和构造线性包含y的所有极值解的问题，y是M（x）的元素。首先，介绍并研究了线性流形的度量算子零件和度量广义逆，然后给出了所有度量的极值或最小极值解的集合的刻画。通过Banach空间的几何方法。本文的主要工具是Banach空间中的广义正交分解定理。 （C）2004由Elsevier Inc.出版

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