Please use this identifier to cite or link to this item: doi:10.22028/D291-26186
Title: Spherical contractions and interpolation problems on the unit ball
Author(s): Eschmeier, Jörg
Putinar, Mihai
Language: English
Year of Publication: 2001
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: In this note fractional representations of multipliers on vector-valued functional Hilbert spaces are used to give a proof of Arveson's version of von Neumann's inequality for n-contractions on the unit ball. We prove a commutant lifting theorem for operators on the classical Hardy space over the unit ball in \mathbb{C}^{n}. As applications we obtain interpolation results for functions in the Schur class, we deduce a Toeplitz corona theorem on the unit ball, and we give a simplified definition of Arveson's curvature invariant for n-contractions with finite-dimensional defect space. In the final part we describe a solution of the operator-valued Nevanlinna-Pick problem with uniform bounds on uniqueness sets in the unit ball.
Link to this record: urn:nbn:de:bsz:291-scidok-43353
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 27
Date of registration: 22-Nov-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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