1. Introduction. Let E be a
Banach space of functions on S, W ⊂ S, and let M(E) be the multiplier algebra of
E. Consider the restriction space E∣W as a quotient of E. The space E has the
Nevanlinna-Pick property relative to W if M(E∣W) = M(E)∣W isometrically;
E has the factorization property relative to W if there exists u ∈ M(E)
such that u is an isometry of E∣W onto the annihilator of S∕W in E. We
consider the problem of characterizing those spaces with the Nevanlinna-Pick
property.