2015 | OriginalPaper | Buchkapitel
Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem
verfasst von : Alexander Gomilko, Yuri Tomilov
Erschienen in: Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics
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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.