Operator algebras of idempotents

We introduce the concept of a matricial Schur ideal, which serves as a dual object for operator algebras generated by a finite set of idempotents. Using matricial Schur ideals and some facturization theorems for tensor products of operator algebras, we are able to obtain matrix-valued interpolation results for general product domains. These results include and generalize the recent matrix-valued interpolation results on the bidisk. (C) 2001 Academic Press.