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Uniformly bounded limit of fractional homomorphisms

Authors:	Pedro J. Miana

Affiliation:	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 . We add this characterization to the Widder-Arendt-Kisynski theorem and relate it to -times integrated semigroups.

Keywords:	Pseudo-resolvents homomorphisms integrated semigroups

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