Hypercyclic subspaces in Fréchet spaces
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Abstract:
In this note, we show that every infinite-dimensional separable Fréchet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of bounded operators when endowed with the strong operator topology. This completes the earlier work of several authors.References
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Additional Information
- L. Bernal-González
- Affiliation: Departamento De Análisis Matemático, Facultad De Matemáticas, Apdo. 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain
- Email: lbernal@us.es
- Received by editor(s): October 6, 2004
- Received by editor(s) in revised form: February 2, 2005
- Published electronically: December 16, 2005
- Additional Notes: The author was partially supported by the Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 and by DGES Grant BFM2003-03893-C02-01.
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1955-1961
- MSC (2000): Primary 47A16; Secondary 47B37
- DOI: https://doi.org/10.1090/S0002-9939-05-08242-0
- MathSciNet review: 2215764
Dedicated: Dedicated to the memory of Professor Miguel de Guzmán, who died in April 2004