Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebras of frequently hypercyclic vectors   We show that the multiples of the backward shift operator on the spaces
$\ell_{p}$, $1\leq p<\infty$, or $c_{0}$, when endowed with coordinatewise
multiplication, do not possess frequently hypercyclic algebras. More generally,
we characterize the existence of algebras of $\mathcal{A}$-hypercyclic vectors
for these operators. We also show that the differentiation operator on the
space of entire functions, when endowed with the Hadamard product, does not
possess frequently hypercyclic algebras. On the other hand, we show that for
any frequently hypercyclic operator $T$ on any Banach space, $FHC(T)$ is
algebrable for a suitable product, and in some cases it is even strongly
algebrable.

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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an