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Uniformly bounded limit of fractional homomorphisms

Authors:	Pedro J Miana

Institution:	Departamento de Matemáticas, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

Abstract:	We show that a bounded homomorphism $T: L^1_{\omega}(\mathbb{R}^+)\to {\mathcal A}$ is equivalent to a uniformly bounded family of fractional homomorphisms $T_{\alpha}: AC^{(\alpha)}_{\omega}(\mathbb{R}^+)\to {\mathcal A}$ for any $\alpha>0$ . We add this characterization to the Widder-Arendt-Kisynski theorem and relate it to $\alpha$ -times integrated semigroups.

Keywords:	Pseudo-resolvents homomorphisms integrated semigroups

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