Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The ideal of p-compact operators: a tensor product approach   We study the space of $p$-compact operators $\mathcal K_p$, using the theory
of tensor norms and operator ideals. We prove that $\mathcal K_p$ is associated
to $/d_p$, the left injective associate of the Chevet-Saphar tensor norm $d_p$
(which is equal to $g_{p'}'$). This allows us to relate the theory of
$p$-summing operators with that of $p$-compact operators. With the results
known for the former class and appropriate hypothesis on $E$ and $F$ we prove
that $\mathcal K_p(E;F)$ is equal to $\mathcal K_q(E;F)$ for a wide range of
values of $p$ and $q$, and show that our results are sharp. We also exhibit
several structural properties of $\mathcal K_p$. For instance, we obtain that
$\mathcal K_p$ is regular, surjective, totally accessible and characterize its
maximal hull $\mathcal K_p^{max}$ as the dual ideal of the $p$-summing
operators, $\Pi_p^{dual}$. Furthermore, we prove that $\mathcal K_p$ coincides
isometrically with $\mathcal {QN}_p^{dual}$, the dual ideal of the quasi
$p$-nuclear operators.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph