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Hypercyclic subspaces in Fréchet spaces


Author: L. Bernal-González
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
Published electronically: December 16, 2005
MathSciNet review: 2215764
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-05-08242-0
Keywords: Hypercyclic operator, hypercyclic sequence, hypercyclic subspace, backward shift, Fr\'echet space.
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.
Dedicated: Dedicated to the memory of Professor Miguel de Guzmán, who died in April 2004
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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