A von Neumann type inequality for certain domains in 𝐂ⁿ

Ambrozie, C.-G.; Timotin, D.

doi:10.1090/S0002-9939-02-06321-9

A von Neumann type inequality for certain domains in $\mathbf C^n$
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by C.-G. Ambrozie and D. Timotin

Proc. Amer. Math. Soc. 131 (2003), 859-869

DOI: https://doi.org/10.1090/S0002-9939-02-06321-9

Published electronically: July 2, 2002

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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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