## 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