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Banach空间中不适定线性算子方程的最佳逼近解 被引量:2

The Best Approximation Solution of Ill-posed Linear Operator Equation in Banach Space
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摘要 设X,Y为Banach空间,T为从X到Y的线性算子.T的值域R(T)≠Y且为逼近紧子空间,T的零空间N(T)≠{θ}.证得不适定算子方程Tx=y的最佳逼近解对任意y∈Y均存在的充分必要条件是N(T)为X的迫近子空间. Let X,Y be Banach space, T be linear operator from X to Y. The range of T, R (T) ≠ Y and R(T) is approximation compact sub-space. The null space of T,N(T) ≠ {θ}. We prove that the best approximation solution of ill-posed operator equation Tx = y exists for every y ∈ Y if and only if N(T) is approximation sub-space of X.
出处 《数学的实践与认识》 CSCD 北大核心 2008年第12期193-196,共4页 Mathematics in Practice and Theory
基金 哈尔滨学院学科基金(Hxk200715) 国家自然科学基金(10671049) 黑龙江教育厅科学技术基金(11531248)
关键词 BANACH空间 不适定线性算子方程 逼近紧 迫近性 最佳逼近紧 Banach space ill-posed linear operator equation approximation compact approximation the best approximation compact
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  • 2Wang Y W, Liu J. Metric generalized inverses for linear manifolds and extremal solutions of linear inclusion in Banach spaces[J]. J Math Anal Appl,2005,302 : 360-371.
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