Abstract
In this paper, we will introduce a new Schur-type product for matrices with operator entries, and explore some of its properties. We shall see a connection between this product and the classical Schur product that will allow us to prove that this set of matrices endowed with such new product defines a Banach algebra. Also, a way to compute the operator and multiplier norms of matrices with operator entries in terms of norms of scalar matrices will be provided. As applications, we present a way to obtain multipliers for one of the products from a multiplier for the other product and show a method to construct a countable amount of elements belonging to different vector measure spaces, from a single element of $$L^\infty (\mathbb {T})$$ .
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