Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complemented subspaces of polynomial ideals   Given the polynomial ideal $\mathcal{J}\circ\mathcal{P} (^{n}E; F)$, we prove
that if $\mathcal{J}\circ\mathcal{P} (^{n}E; F)$ contains an isomorphic copy of
$c_{0}$, then $\mathcal{J}\circ\mathcal{P} (^{n}E; F)$ is not complemented in
$\mathcal{P} (^{n}E; F)$ for every closed operator ideal $\mathcal{J}\subset
\mathcal{L}_{K}$ and every $n\in\mathbb{N}$. Likewise we show that if
$\widehat{(\mathcal{J}\circ\mathcal{L})^{fac}}(^{n}E;F)$ contains an isomorphic
copy of $c_{0}$, then $\widehat{(\mathcal{J}\circ\mathcal{L})^{fac}}(^{n}E;F)$
is not complemented in $\mathcal{P}(^{n}E; F)$ for every closed operator ideal
$\mathcal{J}\subset \mathcal{L}_{K}$ and every $n>1$. When
$\mathcal{J}=\mathcal{L}_{K}$, these results generalizes results of several
authors \cite{LEW},\cite{EM},\cite{KALTON},\cite{IOANA},\cite{SERGIO}, among
others.

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The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: supr-con
7
The categories of this paper are: hep-th