Subordination for sequentially equicontinuous equibounded $$C_0$$-semigroups
Karsten Kruse, Jan Meichsner, Christian Seifert · Journal of Evolution Equations · 2021
Abstract We consider operators A on a sequentially complete Hausdorff locally convex space X such that $$-A$$ - A generates a (sequentially) equicontinuous equibounded $$C_0$$ C 0 -semigroup. For every Bernstein function f we show that $$-f(A)$$ - f ( A ) generates a semigroup which is of the same ‘kind’ as the one generated by $$-A$$ - A . As a special case we obtain that fractional powers $$-A^{\alpha }$$ - A α , where $$\alpha \in (0,1)$$ α ∈ ( 0 , 1 ) , are generators.