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The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces
Published online by Cambridge University Press: 23 November 2015
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.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 3 , August 2016 , pp. 801 - 810
- Copyright
- Copyright © Edinburgh Mathematical Society 2015