Perturbation results for exponentially dichotomous operators on general Banach spaces
type: Item
instance of: scholarly article
title: Perturbation results for exponentially dichotomous operators on general Banach spaces
zbMATH Open document ID: 1069.47014
author: André C. M. Ran
author: C. van der Mee
published in: Journal of Functional Analysis
publication date: 2004-08-16T00:00:00Z
review text: The authors consider the additive perturbation for exponentially dichotomous operators on a Banach space. Let \(-S_0\) be an exponentially dichotomous and \(\Gamma\) a bounded operator on a Banach space. Supposing that either \(\Gamma\) is compact or \(-S_0\) has immediately norm continuous constituent semigroups, it is proved that \(-S = S_0+G\) is also exponentially dichotomous with similar properties as \(-S_0\). Under these conditions, the authors then show that the existence of solutions of Riccati equations associated to block operators is closely connected to the canonical factorizability of the fractional linear function composed of unperturbed and perturbed exponentially dichotomous operators.
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 2091744
zbMATH Keywords: block operator
zbMATH Keywords: exponential dichotomy
zbMATH Keywords: semigroup perturbation
zbMATH Keywords: Riccati equations
MaRDI profile type: Publication
full work available at URL: j.jfa.2003.07.008
OpenAlex ID: W1966426041
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DOI: 10.1016/J.JFA.2003.07.008
description: scientific article; zbMATH DE number 2091744