Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces
type: Item
instance of: scholarly article
title: Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces
zbMATH Open document ID: 1133.47011
author: Hao Zhang
author: Yuwen Wang
published in: Linear Algebra and its Applications
publication date: 2007-09-13T00:00:00Z
review text: The authors consider a perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces. Let \(X\) and \(Y\) be two Banach spaces and let \(C(X,Y)\) and \(B(X,Y)\) denote the homogeneous set of all closed linear operators and the Banach space of all bounded linear operators from \(X\) into \(Y\), respectively. For \(T\in C(X,Y)\) with a closed range \(R(T)\) and a dense domain, the authors define the oblique projection generalized inverse \(T^+\in B(Y,X)\) of \(T\) in a similar way to the Moore--Penrose inverse. The main result in the paper is an explicit expression of the oblique projection generalized inverse \(T^+\) of a closed linear operator \(T\in C(X,Y)\) and an error estimate under \(T\)-bounded perturbation of \(T^+\).
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47A58
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 5190755
zbMATH Keywords: Banach space
zbMATH Keywords: closed linear operator
zbMATH Keywords: oblique projection generalized inverse
zbMATH Keywords: perturbation analysis
MaRDI profile type: Publication
full work available at URL: j.laa.2007.02.025
OpenAlex ID: W1967632380
cites work: Perturbation of operators and applications to frame theory
cites work: Perturbation analysis of the least squares solution in Hilbert spaces
cites work: Perturbation analysis for the operator equation \(Tx=b\) in Banach spaces
cites work: Operators with Closed Range, Pseudo-Inverses, and Perturbation of Frames for a Subspace
cites work: On the perturbation of the least squares solutions in Hilbert spaces
cites work: Perturbation of generalized inverses of linear operators in Hilbert spaces
cites work: New perturbation results on pseudo-inverses of linear operators in Banach spaces
cites work: Q3312749
cites work: Rank theorems of operators between Banach spaces
cites work: Perturbation analysis of generalized inverses of linear operators in Banach spaces
cites work: A generalized preimage theorem in global analysis
cites work: Inner, outer, and generalized inverses in banach and hilbert spaces
cites work: Convergence of Newton-like methods for singular operator equations using outer inverses
cites work: Q4087104
cites work: Metric generalized inverse for linear manifolds and extremal solutions of linear inclusion in Banach spaces
cites work: Metric generalized inverse of linear operator in Banach space
DOI: 10.1016/J.LAA.2007.02.025
description: scientific article; zbMATH DE number 5190755