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

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...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2003-03, Vol.131 (3), p.859-869
Main Authors: Ambrozie, C.-G., Timotin, D.
Format: Article
Language:English
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Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-02-06321-9