Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization of $(\mathcal{I}, \mathcal{J})$-regular matrices   Let $\mathcal{I},\mathcal{J}$ be two ideals on $\mathbf{N}$ which contain the
family $\mathrm{Fin}$ of finite sets. We provide necessary and sufficient
conditions on the entries of an infinite real matrix $A=(a_{n,k})$ which maps
$\mathcal{I}$-convergent bounded sequences into $\mathcal{J}$-convergent
bounded sequences and preserves the corresponding ideal limits. The well-known
characterization of regular matrices due to Silverman--Toeplitz corresponds to
the case $\mathcal{I}=\mathcal{J}=\mathrm{Fin}$.
  Lastly, we provide some applications to permutation and diagonal matrices,
which extend several known results in the literature.

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The categories of this paper are: hep-th
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc