Spectral conditions for stability of one-parameter semigroups
type: Item
instance of: scholarly article
title: Spectral conditions for stability of one-parameter semigroups
zbMATH Open document ID: 0876.47046
author: Charles J. K. Batty
published in: Journal of Differential Equations
publication date: 1996-07-09T00:00:00Z
review text: The author proves the following theorem: Let \(\{S(t)\), \(t\geq 0\}\) be a \(C_0\)-semigroup of linear operators on a Banach space \(Y\) with generator \(B\) and let \(\{T(t)\), \(t\geq 0\}\) be a bounded \(C_0\)-semigroup of linear operators on a Banach space \(X\) with generator \(A\). Let \(\sigma(B)\cap i\mathbb{R}\) be countable, let \(P\sigma(A^*)\cap i\mathbb{R}\) be empty, and let there exist a bounded linear operator \(C:Y\to X\) with dense range which interwines the two semigroups (that is, \(CS(t)=T(t)C\) for all \(t\geq O\)). Then \(|T(t)x|\to 0\) as \(t\to\infty\) for each \(x\) in \(X\).
reviewed by: Glenn Webb
Mathematics Subject Classification ID: 47H20
zbMATH DE Number: 881702
zbMATH Keywords: stability of one-parameter semigroups
zbMATH Keywords: \(C_ 0\)-semigroup of linear operators on a Banach space
zbMATH Keywords: generator
MaRDI profile type: Publication
OpenAlex ID: W2092625031
DOI: 10.1006/JDEQ.1996.0062
description: scientific article; zbMATH DE number 881702