Densely hereditarily hypercyclic sequences and large hypercyclic manifolds

Bernal-González, Luis

doi:10.1090/S0002-9939-99-05185-0

Densely hereditarily hypercyclic sequences and large hypercyclic manifolds
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by Luis Bernal-González

Proc. Amer. Math. Soc. 127 (1999), 3279-3285

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

Published electronically: May 13, 1999

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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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