Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the structure of tensor products of l_p spaces   We examine some structural properties of (injective and projective) tensor
products of $\ell_p$-spaces (projections, complemented subspaces, reflexivity,
isomorphisms, etc.). We combine these results with combinatorial arguments to
address the question of primarity for these spaces and their duals.
  Our main results are: \medbreak \item{(1)} If $1<p<\infty$, then
$B(\ell_p)\approx B(L_p)$ ($B(X)$ consists of the bounded linear operators on
$X$). \medbreak \item{(2)} If ${1\over p_i}+{1\over p_j}\leq1$ for every $i\neq
j$, or if all of the $p_i$'s are equal, then $\ell_{p_1}\hat{\otimes}\cdots
\hat{\otimes}\ell_{p_N}$ is primary. \medbreak \item{(3)} $\ell_p$ embeds into
$\ell_{p_1}\hat{\otimes}\cdots \hat{\otimes}\ell_{p_N}$ if and only if there
exists $A\subset \{1,2,\cdots,n\}$ such that ${1\over p}=\min\{\sum_{i\in
A}{1\over p_i},1\}$. \medbreak \item{(4)} If $1\leq p<\infty$ and $m\geq1$,
then the space of homogeneous analytic polynomials ${\cal P}_m(\ell_p)$ and the
symmetric tensor product of $m$ copies of $\ell_p$ are primary.

3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex