The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces

The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces

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 spac...

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Veröffentlicht in:Proceedings of the Edinburgh Mathematical Society 2016-08, Vol.59 (3), p.801-810
1. Verfasser: Wegner, Sven-Ake
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Banach spaces
Concretes
Group theory
Inequalities
Mathematical analysis
Mathematics
Spectra
Spectrum analysis
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Zusammenfassung: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.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091515000310