The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces

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Abstract

We introduce the concepts of growth and spectral bound for strongly continuous semigroups acting on Fréchet spaces and show that the Banach space inequality s(A) ≠ ω 0(T) extends to the new setting. Via a concrete example of an even uniformly continuous semigroup, we illustrate that for Fréchet spaces effects with respect to these bounds may happen that cannot occur on a Banach space.

Original languageEnglish
Pages (from-to)801-810
Number of pages10
JournalProceedings of the Edinburgh Mathematical Society
Volume59
Issue number3
DOIs
Publication statusE-pub ahead of print - 23 Nov 2015

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