Cyclic behavior of the Cesàro operator on $L_2(0,\infty )$
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- by M. González and F. León-Saavedra PDF
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Abstract:
In this paper we study the cyclic properties of the infinite continuous Cesàro operator defined on $L^2(0,\infty )$ by $(C_\infty f)(x)=\frac {1}{x}\int _0^x f(s) ds$. Despite this operator being cyclic, we show that it is not supercyclic; even more, it is not weakly supercyclic. These results complement some recent ones on the cyclic behavior of Cesàro operators.References
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Additional Information
- M. González
- Affiliation: Department of Mathematics, University of Cantabria, Facultad de Ciencias, Avda. de los Castros s/n, E-39071-Santander, Spain
- MR Author ID: 219505
- Email: gonzalem@unican.es
- F. León-Saavedra
- Affiliation: Department of Mathematics, University of Cádiz, Avda. de la Universidad s/n, E-11405-Jerez de la Frontera, Spain
- Email: fernando.leon@uca.es
- Received by editor(s): July 21, 2008
- Published electronically: January 29, 2009
- Additional Notes: The first author was partially supported by Plan Nacional I+D, Grant MTM-2007-67994
The second author was partially supported by Plan Nacional I+D, Junta de Andalucía FQM-257, and a Grant of Ministerio de Educación y Ciencia. - Communicated by: Michael T. Lacey
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2049-2055
- MSC (2000): Primary 47B37; Secondary 47B38, 47B99
- DOI: https://doi.org/10.1090/S0002-9939-09-09833-5
- MathSciNet review: 2480286