Relatively bounded extensions of generator perturbations
type: Item
instance of: scholarly article
title: Relatively bounded extensions of generator perturbations
zbMATH Open document ID: 1181.47048
DOI: 10.1216/RMJ-2009-39-3-947
published in: Rocky Mountain Journal of Mathematics
publication date: 2009-06-18T00:00:00Z
review text: Let \(A\) be the generator of a \(C_0\)-semigroup \(T(t)\) on a Banach space \(X\), \(D\subset {\mathcal D}(A)\) be a dense subspace of \(X\) such that \(T(t)D\subset D\) for all \(t\geq 0\), and \(B_0:D\to Y\) be a linear operator from \(D\) to a Banach space \(Y\) such that \(B_0T(\cdot)\) is continuous for each \(x\in D\). The authors characterize the extendability of \(B_0\) to an \(A\)-bounded operator \(B:{\mathcal D}(A)\to Y\) by conditions similar to but weaker than the Miyadera condition (in the well-known Miyadera perturbation theorem). They also treat the relatively bounded extension problem for the case when \(A\) is a Hille-Yosida operator in \(X\).
reviewed by: Ti-Jun Xiao
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47D62
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 47B60
zbMATH DE Number: 5566210
zbMATH Keywords: strongly continuous semigroup
zbMATH Keywords: perturbation theory
zbMATH Keywords: Miyadera perturbation
zbMATH Keywords: relative bound
zbMATH Keywords: Hille-Yosida operator
zbMATH Keywords: positive perturbation
author: Horst R. Thieme
author: Jürgen Voigt
MaRDI profile type: Publication
cites work: Q2716079
cites work: Q5549343
cites work: Perturbing semigroups by solving Stieltjes renewal equations
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: Q3244654
cites work: Q4453335
cites work: On perturbation theory for semi-groups of operators
cites work: Q4321878
cites work: Multiplicative perturbations of \(C_ 0\)-semigroups and some applications to step responses and cumulative outputs
cites work: Q4715322
cites work: On the perturbation theory for strongly continuous semigroups
cites work: On resolvent positive operators and positive \(C_ 0\)-semigroups on AL- spaces
description: scientific article; zbMATH DE number 5566210