Necessary and sufficient conditions for the inversion of linearly-perturbed bounded linear operators on Banach space using Laurent series
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for the inversion of linearly-perturbed bounded linear operators on Banach space using Laurent series
zbMATH Open document ID: 1223.47014
author: A. R. Albrecht
author: Phil Howlett
author: Charles E. M. Pearce
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-07-18T00:00:00Z
review text: Using a Laurent series representation, the authors present a detailed discussion of necessary and sufficient conditions for the inversion of linearly-perturbed bounded linear operators on Banach space that are singular in the unperturbed state. In fact, the main purpose of this paper is to complete the analysis of the conditions under which the inverse of a linearly-perturbed operator can be represented by a Laurent series with a finite-order pole at the orgin. The most relevant references are the two papers [\textit{P. Howlett, K. Avrachenkov, C. Pearce} and \textit{V. Ejov}, J. Math. Anal. Appl. 353, No.~1, 68--84 (2009; Zbl 1216.47020); \textit{P. Howlett, A. Albrecht} and \textit{C. Pearce}, J. Math. Anal. Appl. 366, No.~1, 112--123 (2010; Zbl 1192.47010)], where the authors first proposed that the inversion could be expressed in terms of corresponding complementary projections in the domain and range spaces.
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 5925609
zbMATH Keywords: Banach space
zbMATH Keywords: complementary subspaces
zbMATH Keywords: linear perturbation
zbMATH Keywords: bounded linear operators
zbMATH Keywords: Laurent series
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.05.007
OpenAlex ID: W2063147174
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DOI: 10.1016/J.JMAA.2011.05.007
description: scientific article; zbMATH DE number 5925609