Proceedings of the American Mathematical Society

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



Porosity and hypercyclic operators

Author: Frédéric Bayart
Journal: Proc. Amer. Math. Soc. 133 (2005), 3309-3316
MSC (2000): Primary 47A16, 28A05
Published electronically: May 9, 2005
MathSciNet review: 2161154
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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.

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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

Keywords: Porous sets, hypercyclic operators
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
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.