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arXiv · 1802.05059

Subordination for sequentially equicontinuous equibounded $C_0$-semigroups

Karsten Kruse·Jan Meichsner·Christian Seifert
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Abstract

We consider operators $A$ on a sequentially complete Hausdorff locally convex space $X$ such that $-A$ generates a (sequentially) equicontinuous equibounded $C_0$-semigroup. For every Bernstein function $f$ we show that $-f(A)$ generates a semigroup which is of the same `kind' as the one generated by $-A$. As a special case we obtain that fractional powers $-A^{\alpha}$, where $\alpha \in (0,1)$, are generators.

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Karsten Kruse, Jan Meichsner, Christian Seifert. 2018-02-14. Subordination for sequentially equicontinuous equibounded $C_0$-semigroups. https://doi.org/10.1007/s00028-021-00700-7

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