Eventual norm continuity for neutral semigroups on Banach spaces

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In this paper we prove, under suitable hypotheses, eventually norm continuity and compactness of the solution semigroups of certain neutral differential equations in Banach spaces. Our approach is based on a general perturbation theorem obtained from closed-loop systems of infinite dimensional control systems with unbounded control and observation operators. In fact, the solution semigroup can be viewed as the semigroup of an appropriate closed-loop system in product state spaces.

Original languageEnglish
Pages (from-to)543-552
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 15 Mar 2011



  • Banach space
  • Compactness
  • Neutral semigroup
  • Norm continuity
  • Perturbation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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