Localizable points in the support of a multiplier ideal and spectra of constrained operators

A unitarily invariant, complete Nevanlinna–Pick kernel K on the unit ball determines a class of operators Hilbert space called K-contractions. We study those K-contractions that are constrained, in sense they annihilated by an ideal multipliers. Our overarching goal is to identify various joint spectra these constrained through vanishing locus their annihilators. methods based around careful analysis subset associated annihilator, which we call its support. For functional models, show how this support completely several natural spectra. The picture more complicated for general K-contractions, as can be properly contained Nevertheless, “localizable” portion always consists spectral points. When assumed small appropriate sense, manage effectively detect points localizability.