Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality

Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov, Hugo J. Woerdeman

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

We obtain a decomposition for multivariable Schur-class functions on the unit polydisk which, to a certain extent, is analogous to Agler's decomposition for functions from the Schur-Agler class. As a consequence, we show that d-tuples of commuting strict contractions obeying an additional positivity constraint satisfy the d-variable von Neumann inequality for an arbitrary operator-valued bounded analytic function on the polydisk. Also, this decomposition yields a necessary condition for solvability of the finite data Nevanlinna-Pick interpolation problem in the Schur class on the unit polydisk.

Original languageEnglish
Pages (from-to)3035-3054
Number of pages20
JournalJournal of Functional Analysis
Volume256
Issue number9
DOIs
StatePublished - 1 May 2009

Keywords

  • Commuting contractions
  • Multivariable Schur class
  • Multivariable von Neumann inequality
  • Nevanlinna-Pick interpolation problem
  • Scattering system
  • Schur-Agler class
  • Unitary dilation

ASJC Scopus subject areas

  • Analysis

Fingerprint

Dive into the research topics of 'Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality'. Together they form a unique fingerprint.

Cite this