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In this paper, we will consider matrices with entries in the space ofoperators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space and considerthe class of matrices that can be approached in the operator norm by matriceswith a finite number of diagonals. We will use the Schur product with Toeplitzmatrices generated by summability kernels to describe such a class and showthat in the case of Toeplitz matrices it can be identified with the space ofcontinuous functions with values in $\mathcal B(H)$. We shall also introducematriceal versions with operator entries of classical spaces of holomorphicfunctions such as $H^\infty(\mathbb{D})$ and $A(\mathbb{D})$ when dealing withupper triangular matrices.

New spaces of matrices with operator entries