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