Resolvent norm decay does not characterize norm continuity
type: Item
instance of: scholarly article
title: Resolvent norm decay does not characterize norm continuity
zbMATH Open document ID: 1188.47035
author: Tamás Mátrai
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
review text: The author studies the norm continuity of \(C_0\)-semigroups in general Banach spaces. He gives an example so that the semigroup is contractive and the resolvent satisfies condition \(\lim_{s\to\infty} \|R(is,A)\|=0\), but the semigroup is not norm continuous, even not eventually norm continuous. In addition, the author shows that the Spectral Mapping Theorem does not hold. This result gives a negative answer for the Pazy question in Banach space.
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 5508713
zbMATH Keywords: semigroup
zbMATH Keywords: norm continuity
reviewed by: Gen Qi Xu
MaRDI profile type: Publication
full work available at URL: s11856-008-1054-6
OpenAlex ID: W1985268106
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DOI: 10.1007/S11856-008-1054-6
description: scientific article; zbMATH DE number 5508713