In this paper we study block matrices and multipliers with respect to a Schur-type product operation on them. A subclass of the block Toeplitz matrices is explored, obtaining generalizations of Toeplitz’s and Bennett’s classical theorems that show identifications with complex functions and measures on the bitorus. We also investigate the classes of matrices that can be approximated in the operator and multiplier norms by a subclass of the polynomial matrices and describe them using matrices generated by two-dimensional summability kernels, paying attention to the case of Toeplitz matrices and finding the corresponding connections with spaces of functions.

在本文中，我们针对块矩阵和乘法器针对其上的Schur型乘积运算进行研究。探索块Toeplitz矩阵的一个子类，获得Toeplitz和Bennett经典定理的一般化，这些定理显示出在比托斯上具有复杂函数和度量的标识。我们还研究了可以由多项式矩阵的子类在算子和乘数范数中近似的矩阵类别，并使用二维可和核生成的矩阵来描述它们，同时注意Toeplitz矩阵的情况并找到对应的连接具有功能空间。