Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal estimates for summing multilinear operators   We show that given a positive integer $m$, a real number $p\in\left[
2,\infty\right)$ and $1\leq s<p^{\ast}$ the set of non--multiple $\left(
r;s\right)$--summing $m$--linear forms on $\ell_{p}\times\cdots\times \ell_{p}$
contains, except for the null vector, a closed subspace of maximal dimension
whenever $r<\frac{2ms}{s+2m-ms}$. This result is optimal since for
$r\geq\frac{2ms}{s+2m-ms}$ all $m$--linear forms on $\ell_{p}\times
\cdots\times\ell_{p}$ are multiple $\left( r;s\right)$--summing. In particular,
among other results, we generalize a result related to cotype (from 2010) due
to Botelho \textit{et al.}

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The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int