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arXiv · 1408.5037

The growth bound for strongly continuous semigroups on Fréchet spaces

Sven-Ake Wegner
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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 $s(A)\leqslantω_0(T)$ 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.

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Sven-Ake Wegner. 2014-08-21. The growth bound for strongly continuous semigroups on Fréchet spaces. https://doi.org/10.1017/s0013091515000310

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