Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse-closedness of the subalgebra of locally nuclear operators   Let $X$ be a Banach space and $T$ be a bounded linear operator acting in
$l_p(\mathbb Z^c,X)$, $1\le p\le\infty$. The operator $T$ is called
\emph{locally nuclear} if it can be represented in the form \begin{equation*}
(Tx)_k=\sum\limits_{m\in\mathbb Z^c} b_{km}x_{k-m},\qquad k\in\mathbb Z^c,
\end{equation*} where $b_{km}:\,X\to X$ are nuclear, \begin{equation*} \lVert
b_{km}\rVert_{\mathfrak S_1}\le\beta_{m},\qquad k,m\in\mathbb Z^c,
\end{equation*} $\lVert\cdot\rVert_{\mathfrak S_1}$ is the nuclear norm,
$\beta\in l_{1}(\mathbb Z^c,\mathbb C)$ or $\beta\in l_{1,g}(\mathbb
Z^c,\mathbb C)$, and $g$ is an appropriate weight on $\mathbb Z^c$. It is
established that if $T$ is locally nuclear and the operator $\mathbf1+T$ is
invertible, then the inverse operator $(\mathbf1+T)^{-1}$ has the form
$\mathbf1+T_1$, where $T_1$ is also locally nuclear. This result is refined for
the case of operators acting in $L_p(\mathbb R^c,\mathbb C)$.

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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: econ