Nevanlinna-Pick interpolation and factorization of linear functionals, Integral Equations Operator Theory 70

Abstract. If A is a unital weak- ∗ closed subalgebra of a mul-tiplier algebra on a reproducing kernel Hilbert space which has property A1(1), then the cyclic invariant subspaces provide an Nevanlinna-Pick (NP) family of kernels. This yields an NP in-terpolation theorem for a wide class of operator algebras. In particular, it applies to many kernel spaces over the unit disk including the Bergman space. We also show that the multiplier algebra of a complete NP space has A1(1), and thus this result applies to all of its subalgebras. A matrix version of this result is also established. It applies, in particular, to all unital weak- ∗ closed subalgebras of H ∞ acting on Hardy space or on Bergman space. 1