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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniformly bounded limit of fractional homomorphisms
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by Pedro J. Miana PDF
Proc. Amer. Math. Soc. 133 (2005), 2569-2575 Request permission

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.
References
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Additional Information
  • Pedro J. Miana
  • Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain
  • MR Author ID: 672733
  • Email: pjmiana@unizar.es
  • Received by editor(s): February 1, 2003
  • Published electronically: March 31, 2005
  • Additional Notes: This work was supported by a grant from Programa Europa, CAI, 2002. This paper was made during a visit to the Charles University in Prague. The author thanks Dr. Eva Fasangova and the Analysis Mathematical Department for the stay in Prague.
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2569-2575
  • MSC (2000): Primary 47D62; Secondary 26A33, 46J25
  • DOI: https://doi.org/10.1090/S0002-9939-05-07978-5
  • MathSciNet review: 2146200