Perturbations of Moore-Penrose metric generalized inverses of linear operators in Banach spaces
type: Item
instance of: scholarly article
title: Perturbations of Moore-Penrose metric generalized inverses of linear operators in Banach spaces
zbMATH Open document ID: 1322.47002
author: Haifeng Ma
author: Shuang Sun
author: Wenjing Zheng
author: Yuwen Wang
publication date: 2014-12-10T00:00:00Z
review text: Let \(X\) be a real Banach space and \(K \subseteq X\). Let \({\mathcal P}_K\) denote the \textit{metric projection} of \(X\) into \(K\). \(K\) is said to be \textit{Chebyshev} if \({\mathcal P}_K(x)\) a singleton for each \(x \in X\). Let \(Y\) be another real Banach space and \(T:D(T) \subseteq X \rightarrow Y\) be a linear map. Let \(N(T)\) and \(R(T)\) denote the null space and the range space of \(T\), respectively. Suppose that \(cl N(T)\) and \(cl R(T)\) are subspaces that are also Chebyshev sets in \(X\) and \(Y\), respectively. If there exists a homogeneous operator \(T^M:D(T^M) \rightarrow D(T)\) such that \(TT^MT=T\) on \(D(T)\), \(T^MTT^M=T^M\) on \(D(T^M)\), \(T^MT=I-{\mathcal P}_{clN(T)}\) on \(D(T)\) and \(TT^M={\mathcal P}_{clR(T)}\) on \(D(T^M)\), then such an operator is unique and is called the Moore-Penrose metric generalized inverse of \(T\). The authors study perturbations of the Moore-Penrose metric generalized inverses and obtain error estimates. A perturbation formula for such a generalized inverse is given in a certain framework.
reviewed by: K. C. Sivakumar
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A55
zbMATH DE Number: 6378951
zbMATH Keywords: Banach space
zbMATH Keywords: Moore-Penrose metric generalized inverse
zbMATH Keywords: perturbation
MaRDI profile type: Publication
full work available at URL: s10114-014-3340-z
OpenAlex ID: W1973826908
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DOI: 10.1007/S10114-014-3340-Z
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 6378951