The best generalised inverse of the linear operator in normed linear space
type: Item
instance of: scholarly article
title: The best generalised inverse of the linear operator in normed linear space
zbMATH Open document ID: 1114.47001
author: Ping Liu
author: Yuwen Wang
published in: Linear Algebra and its Applications
publication date: 2007-02-14T00:00:00Z
review text: Let \(X\), \(Y\) be normed linear spaces and let \(A\) be a bounded linear operator from \(X\) into \(Y\). There is given a construction of a best approximate solution of the equation \(Ax= y\) in the case when \(A\) is not invertible, \(y\in Y\). This solution, in general, does not depend linearly on \(y\).
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 5126046
zbMATH Keywords: best generalized inverse
zbMATH Keywords: normed space
zbMATH Keywords: reflexive Banach space
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: linear equation
reviewed by: Danuta Przeworska-Rolewicz
MaRDI profile type: Publication
full work available at URL: j.laa.2006.04.024
OpenAlex ID: W2008995872
cites work: Q4159877
cites work: Geometry of Banach spaces. Selected topics
cites work: The best generalized inverse
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cites work: Q4020227
cites work: Q5298089
cites work: Metric generalized inverse for linear manifolds and extremal solutions of linear inclusion in Banach spaces
cites work: An approximation problem of the finite rank operator in Banach spaces
cites work: Metric generalized inverse of linear operator in Banach space
DOI: 10.1016/J.LAA.2006.04.024
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description: scientific article; zbMATH DE number 5126046