Coincidence of Schur multipliers of the drury-arveson space

Abstract

In a purely multi-variable setting (i.e., the issues discussed in this note are not interesting in the single variable operator theory setting), we show that the coincidence of two operator valued Schur class multipliers of a certain kind on the Drury-Arveson space is characterized by the fact that the associated colligations (or a variant, obtained canonically) are `unitarily coincident' in a sense to be made precise in the last section of this article.