Uniformly bounded limit of fractional homomorphisms

Miana, Pedro

doi:10.1090/S0002-9939-05-07978-5

Uniformly bounded limit of fractional homomorphisms
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by Pedro J. Miana

Proc. Amer. Math. Soc. 133 (2005), 2569-2575

DOI: https://doi.org/10.1090/S0002-9939-05-07978-5

Published electronically: March 31, 2005

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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-Kisyński theorem and relate it to $\alpha$-times integrated semigroups.

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