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Uniformly bounded limit of fractional homomorphisms

Author: Pedro J. Miana
Journal: Proc. Amer. Math. Soc. 133 (2005), 2569-2575
MSC (2000): Primary 47D62; Secondary 26A33, 46J25
Published electronically: March 31, 2005
MathSciNet review: 2146200
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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-Kisynski theorem and relate it to $\alpha$-times integrated semigroups.

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Additional Information

Pedro J. Miana
Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

Keywords: Pseudo-resolvents, homomorphisms, integrated semigroups
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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