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 this article.

AMS Subject Classification (1991): 47A13, 47A56

Keyword(s): weakly coisometric realizations, Schur class, Drury--Arveson space, de Branges--Rovnyak space

Received June 9, 2010, and in revised form November 10, 2010. (Registered under 37/2010.)