Porosity and hypercyclic operators
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Abstract:
We study if the set of hypercyclic vectors of a hypercyclic operator is the complement of a $\sigma$-porous set. This leads to interesting results for both points of view: a limitation of the size of hypercyclic vectors, and new examples of first category sets which are not $\sigma$-porous.References
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Additional Information
- Frédéric Bayart
- Affiliation: Laboratoire Bordelais d’Analyse et de Géométrie, UMR 5467, Université Bordeaux 1, 351 Cours de la Libération, F-33405 Talence cedex, France
- MR Author ID: 683115
- Email: bayart@math.u-bordeaux.fr
- Received by editor(s): January 27, 2004
- Received by editor(s) in revised form: June 17, 2004
- Published electronically: May 9, 2005
- Communicated by: Joseph A. Ball
- © 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), 3309-3316
- MSC (2000): Primary 47A16, 28A05
- DOI: https://doi.org/10.1090/S0002-9939-05-07842-1
- MathSciNet review: 2161154