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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A von Neumann type inequality for certain domains in $\mathbf C^n$


Authors: C.-G. Ambrozie and D. Timotin
Journal: Proc. Amer. Math. Soc. 131 (2003), 859-869
MSC (2000): Primary 47A13, 47A57
Published electronically: July 2, 2002
MathSciNet review: 1937424
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Abstract: Strict contractions on a Hilbert space have a functional calculus with functions that are analytic in the unit disc of the complex plane; an estimate of the norm is then provided by von Neumann's inequality. We consider functions that satisfy related inequalities with respect to multioperators connected to certain domains in ${\mathbf C}^n$; a representation formula and a Nevanlinna-Pick type theorem are obtained.


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Additional Information

C.-G. Ambrozie
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania
Email: cambroz@stoilow.imar.ro

D. Timotin
Affiliation: Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania
Email: dtimotin@stoilow.imar.ro

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06321-9
PII: S 0002-9939(02)06321-9
Keywords: Von Neumann inequality, multioperators, Nevanlinna--Pick problem
Received by editor(s): December 12, 2000
Received by editor(s) in revised form: February 19, 2001, and October 17, 2001
Published electronically: July 2, 2002
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society