The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces

Sven Ake Wegner

Research output: Contribution to journalArticle

1 Citation (Scopus)

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) ⩽ ω0(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)1-10
Number of pages10
JournalProceedings of the Edinburgh Mathematical Society
DOIs
Publication statusAccepted/In press - Nov 23 2015
Externally publishedYes

Fingerprint

Strongly Continuous Semigroups
Banach space
Spectral Bound
Uniformly continuous
Semigroup
Concepts

Keywords

  • Fréchet space
  • growth bound
  • power-bounded operator
  • semigroup
  • spectral bound

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces. / Wegner, Sven Ake.

In: Proceedings of the Edinburgh Mathematical Society, 23.11.2015, p. 1-10.

Research output: Contribution to journalArticle

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