Universal interpolating sets and the Nevanlinna-Pick property in Banach spaces of functions

A. K. Snyder

Vol. 76 (1978), No. 2, 513–525

DOI: 10.2140/pjm.1978.76.513

Abstract

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.

Mathematical Subject Classification 2000

Primary: 46E99

Secondary: 46J15

Milestones

Received: 23 August 1977

Published: 1 June 1978