2010/08/05 by Kenneth R. Davidson, Davidson, Kenneth R., Ryan Hamilton +1
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.FA #math.OA
paper · pdf · doi:10.48550/arxiv.1008.1090
26 pages; minor revisions; to appear in Integral Equations and Operator Theory
openalex publication_date 2010/08/05 · arxiv created 2011/01/06 · arxiv updated 2011/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If \fA is a unital weak-* closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property \bA1(1), then the cyclic invariant subspaces index a Nevanlinna-Pick family of kernels. This yields an NP interpolation theorem for a wide class of algebras. In particular, it applies to many function spaces over the unit disk including Bergman space. We also show that the multiplier algebra of a complete NP space has \bA1(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.