Perturbations of generators of <textbox>C₀textbox>-semigroups and resolvent decay

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• 作者：Charles J.K. Batty ; Sebastian Kró ; l
• 关键词：Perturbation ; Resolvent ; style=""text-decoration ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4Y889W9-1&_mathId=mml4&_user=10&_cdi=6894&_pii=S0022247X10000879&_rdoc=11&_issn=0022247X&_acct=C000050221&_vers
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2010
• 出版时间：15 July 2010
• 年：2010
• 卷：367
• 期：2
• 页码：434-443
• 全文大小：208 K

文摘

We obtain new stability results for those properties of C₀-semigroups which admit characterisation in terms of decay of resolvents of infinitesimal generators on vertical lines, e.g. analyticity, Crandall–Pazy differentiability or immediate norm continuity in the case of Hilbert spaces. As a consequence we get a generalisation of the Kato–Neuberger theorem on approximation of the identity. Finally, we present examples shedding a new light on resolvent characterisation of eventually differentiable C₀-semigroups for which differentiability is stable under bounded perturbations.