论文标题
$（\ Mathcal {i}，\ Mathcal {J}）$的特征 - 常规矩阵
A characterization of $(\mathcal{I}, \mathcal{J})$-regular matrices
论文作者
论文摘要
令$ \ mathcal {i}，\ Mathcal {j} $是$ \ Mathbf {n} $的两个理想，其中包含有限集的family $ \ mathrm {fin} $。我们在无限的真实矩阵$ a =（a_ {n，k}）$的条目上提供了必要和足够的条件，该$映射$ \ Mathcal {i} $ - convergent界限序列$ \ MATHCAL {J} $ - 转化为有限序列，并保留相应的理想限制。由Silverman引起的常规矩阵的众所周知的表征与$ \ Mathcal {i} = \ Mathcal {J} = \ Mathrm {Fin} $相对应。 最后，我们为置换和对角线矩阵提供了一些应用，这些矩阵扩展了文献中的几个已知结果。
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.
