Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503258 | Journal of Mathematical Analysis and Applications | 2005 | 12 Pages |
Abstract
Let X,Y be Banach spaces and M a linear manifold in XÃY={{x,y}â£xâX,yâY}. 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 yâM(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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yuwen Wang, Jing Liu,