Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality |
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Authors: | Anatolii Grinshpan Victor Vinnikov |
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Institution: | a Department of Mathematics, Drexel University, 3141 Chestnut St., Philadelphia, PA 19104, USA b Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel |
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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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Keywords: | Multivariable von Neumann inequality Commuting contractions Unitary dilation Multivariable Schur class Schur-Agler class Scattering system Nevanlinna-Pick interpolation problem |
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