Hypercyclic subspaces in Fréchet spaces

Bernal-González, L.

doi:10.1090/S0002-9939-05-08242-0

Hypercyclic subspaces in Fréchet spaces
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Proc. Amer. Math. Soc. 134 (2006), 1955-1961 Request permission

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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