TY - GEN
T1 - Spherical contractions and interpolation problems on the unit ball
A1 - Eschmeier,Jörg
A1 - Putinar,Mihai
Y1 - 2011/11/22
N2 - 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.
CY - Saarbrücken
PB - Saarländische Universitäts- und Landesbibliothek
AD - Postfach 151141, 66041 Saarbrücken
UR - http://scidok.sulb.uni-saarland.de/volltexte/2011/4335
ER -