TY - JOUR
T1 - Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality
AU - Grinshpan, Anatolii
AU - Kaliuzhnyi-Verbovetskyi, Dmitry S.
AU - Vinnikov, Victor
AU - Woerdeman, Hugo J.
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (A. Grinshpan), [email protected] (D.S. Kaliuzhnyi-Verbovetskyi), [email protected] (V. Vinnikov), [email protected] (H.J. Woerdeman). 1 Partially supported by NSF grant DMS-0500678.
PY - 2009/5/1
Y1 - 2009/5/1
N2 - 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.
AB - 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.
KW - Commuting contractions
KW - Multivariable Schur class
KW - Multivariable von Neumann inequality
KW - Nevanlinna-Pick interpolation problem
KW - Scattering system
KW - Schur-Agler class
KW - Unitary dilation
UR - http://www.scopus.com/inward/record.url?scp=62049083749&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2008.09.012
DO - 10.1016/j.jfa.2008.09.012
M3 - Article
AN - SCOPUS:62049083749
SN - 0022-1236
VL - 256
SP - 3035
EP - 3054
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 9
ER -