A CHARACTERIZATION OF PICK BODIES

Let z = (z(1),...,Z(n)) be an n-tuple of distinct points in the open unit disk. We define the Pick body D(z) as the totality of points w = (w(1),..., W-n) in C-n such that there exists f is an element of H-infinity with parallel to f parallel to(infinity) less than or equal to 1 and f(z(j)) = w(j), for 1 less than or equal to j less than or equal to n. We discuss the properties of Pick bodies and characterize them among compact subsets of C-n. We also study related questions concerning certain algebras of operators on Hilbert space.