Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypercyclic subspaces on Fr\'echet spaces without continuous norm   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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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc