Uniformly bounded limit of fractional homomorphisms

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 t...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2005-09, Vol.133 (9), p.2569-2575
Main Author: MIANA, Pedro J
Format: Article
Language:English
Subjects:
Algebra
Approximation
Banach space
Exact sciences and technology
Functional analysis
Homomorphisms
Laplace transformation
Mathematical analysis
Mathematical theorems
Mathematics
Operator theory
Real functions
Sciences and techniques of general use
Semigroups
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-07978-5