\(C_0\)-semigroups norm continuous at infinity
type: Item
instance of: scholarly article
title: \(C_0\)-semigroups norm continuous at infinity
zbMATH Open document ID: 0927.47029
DOI: 10.1007/BF02574097
published in: Semigroup Forum
publication date: 1999-12-13T00:00:00Z
full work available at URL: https://eudml.org/doc/135449
review text: The authors study a class of \(C_0\)-semigroups for which the spectral mapping theorem holds and the spectral bound and growth bound coincide. The crucial condition is norm continuity ``at infinity'' which means that \[ \lim_{t\to\infty} \limsup_{s\to 0}\| e^{-t\omega(A)} T(t)(I- e^{-s\omega(A)}T(s))\|= 0. \]
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47D60
zbMATH DE Number: 858475
zbMATH Keywords: norm continuity at infinity
zbMATH Keywords: \(C_0\)-semigroups
zbMATH Keywords: spectral mapping theorem
zbMATH Keywords: spectral bound
zbMATH Keywords: growth bound
author: Josep Martínez
author: J. M. Mazón
reviewed by: Jürgen Appell
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 858475