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arXiv · 1302.6447

Hypercyclic subspaces on Fr\'echet spaces without continuous norm

Quentin Menet
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Abstract

Known results about hypercyclic subspaces concern either Fr\'echet spaces with a continuous norm or the space \omega. We fill the gap between these spaces by investigating Fr\'echet spaces without continuous norm. To this end, we divide hypercyclic subspaces into two types: the hypercyclic subspaces M for which there exists a continuous seminorm p such that M\cap \ker p=\{0\} and the others. For each of these types of hypercyclic subspaces, we establish some criteria. This investigation permits us to generalize several results about hypercyclic subspaces on Fr\'echet spaces with a continuous norm and about hypercyclic subspaces on \omega. In particular, we show that each infinite-dimensional separable Fr\'echet space supports a mixing operator with a hypercyclic subspace.

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Quentin Menet. 2013-02-26. Hypercyclic subspaces on Fr\'echet spaces without continuous norm. https://doi.org/10.1007/s00020-013-2096-7

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