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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A von Neumann type inequality for certain domains in $\mathbf C^n$
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by C.-G. Ambrozie and D. Timotin PDF
Proc. Amer. Math. Soc. 131 (2003), 859-869 Request permission

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.
References
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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
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 859-869
  • MSC (2000): Primary 47A13, 47A57
  • DOI: https://doi.org/10.1090/S0002-9939-02-06321-9
  • MathSciNet review: 1937424