Journal article
Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality
Journal of functional analysis, v 256(9), pp 3035-3054
2009
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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.
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Details
- Title
- Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality
- Creators
- Anatolii Grinshpan - Drexel UniversityDmitry S. Kaliuzhnyi-Verbovetskyi - Drexel UniversityVictor Vinnikov - Ben-Gurion University of the NegevHugo J. Woerdeman - Drexel University
- Publication Details
- Journal of functional analysis, v 256(9), pp 3035-3054
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000265126800011
- Scopus ID
- 2-s2.0-62049083749
- Other Identifier
- 991019168254804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics