Matrix Multipliers for a Block Schur Product

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.