Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Translation-finite sets, and weakly compact derivations from
  $\lp{1}(\Z_+)$ to its dual   We characterize those derivations from the convolution algebra
$\ell^1({\mathbb Z}_+)$ to its dual which are weakly compact. In particular, we
provide examples which are weakly compact but not compact. The characterization
is combinatorial, in terms of "translation-finite" subsets of ${\mathbb Z}_+$,
and we investigate how this notion relates to other notions of "smallness" for
infinite subsets of ${\mathbb Z}_+$. In particular, we show that a set of
strictly positive Banach density cannot be translation-finite; the proof has a
Ramsey-theoretic flavour.

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The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: cond-mat