On a theorem of Rolewicz for semigroups of operators in locally convex spaces
type: Item
instance of: scholarly article
title: On a theorem of Rolewicz for semigroups of operators in locally convex spaces
zbMATH Open document ID: 1004.47023
author: Alin Pogan
author: Mihail Megan
published in: Annales Mathématiques Blaise Pascal
publication date: 2003-01-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/79215
review text: \textit{R. Datko} [J. Math. Anal. Appl. 32, 610-616 (1970; Zbl 0211.16802)] characterized uniform exponential stability of \(C_0\)-semigroup \((T(t))_{t \geq 0}\) on a Banach space \(X\) by the integrability condition \(\int_0^\infty \|T(t) x\|dt < X\). This result, and its various generalizations [see \textit{J. M. A. M. v. Neerven}, ``The asymptotic behaviour of semigroups of linear operators'' (1996; Zbl 0905.47001)], is extended to semigroups on locally convex spaces.
reviewed by: Rainer Nagel
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 1501761
zbMATH Keywords: uniform exponential stability
zbMATH Keywords: \(C_0\)-semigroup
zbMATH Keywords: integrability condition
MaRDI profile type: Publication
OpenAlex ID: W2068272871
cites work: Extending a theorem of A. M. Liapunov to Hilbert space
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DOI: 10.5802/AMBP.122
description: scientific article; zbMATH DE number 1501761