Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem

Abstract

Using functional calculi theory, we obtain several estimates for $\|\psi(A)g(A)\|$, where ψ is a Bernstein function, g is a bounded completely monotone function and −A is the generator of a holomorphic C₀-semigroup on a Banach space, bounded on $[0,\infty)$. Such estimates are of value, in particular, in approximation theory of operator semigroups. As a corollary, we obtain a new proof of the fact that $-\psi{A}$ generates a holomorphic semigroup whenever −A does, established recently in [8] by a different approach.

To Charles Batty, colleague and friend, on the occasion of his sixtieth anniversary with admiration

Mathematics Subject Classification (2010). Primary 47A60, 65J08, 47D03; Secondary 46N40, 65M12