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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Densely hereditarily hypercyclic sequences
and large hypercyclic manifolds


Author: Luis Bernal-González
Journal: Proc. Amer. Math. Soc. 127 (1999), 3279-3285
MSC (1991): Primary 47B99; Secondary 46A99, 30E10, 32A07
Published electronically: May 13, 1999
MathSciNet review: 1646318
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Abstract: We prove in this paper that if $(T_{n})$ is a hereditarily hypercyclic sequence of continuous linear mappings between two topological vector spaces $X$ and $Y$, where $Y$ is metrizable, then there is an infinite-dimensional linear submanifold $M$ of $X$ such that each non-zero vector of $M$ is hypercyclic for $(T_{n})$. If, in addition, $X$ is metrizable and separable and $(T_{n})$ is densely hereditarily hypercyclic, then $M$ can be chosen dense.


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Additional Information

Luis Bernal-González
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain
Email: lbernal@cica.es

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05185-0
PII: S 0002-9939(99)05185-0
Keywords: Hypercyclic vector, linear operator, densely hereditarily hypercyclic sequence, infinite-dimensio\-nal manifold, dense manifold, metrizable topological vector space, entire function of subexponential type, Runge domain, infinite order linear differential operator
Received by editor(s): February 2, 1998
Published electronically: May 13, 1999
Additional Notes: This research was supported in part by DGES grant #PB96–1348 and the Junta de Andalucía
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society