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 factorization 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.