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 hdl:20.500.11880/26242 http://dx.doi.org/10.22028/D291-26186 |
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 |
Files for this record:
File | Description | Size | Format | |
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preprint_27_01.pdf | 308,71 kB | Adobe PDF | View/Open |
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