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

DOI:
https://doi.org/10.1090/S0002-9939-99-05185-0

Published electronically:
May 13, 1999

MathSciNet review:
1646318

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove in this paper that if is a hereditarily hypercyclic sequence of continuous linear mappings between two topological vector spaces and , where is metrizable, then there is an infinite-dimensional linear submanifold of such that each non-zero vector of is hypercyclic for . If, in addition, is metrizable and separable and is densely hereditarily hypercyclic, then 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:
https://doi.org/10.1090/S0002-9939-99-05185-0

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