Schur product with operator-valued entries

Abstract

In this paper we characterize Toeplitz matrices with entries in the space of bounded operators on Hilbert spaces $\mathcal{B}(H)$ which define bounded operators acting on ${\ell }^2(H)$ and use it to get the description of the right Schur multipliers acting on ${\ell }^2(H)$ in terms of certain operator-valued measures.