Journal of Operator Theory

Volume 41, Issue 2, Spring 1999 pp. 365-389.

Standard models under polynomial positivity conditions

Authors: Sandra Pott
Author institution: Fachbereich Mathematik, Universitaet des Saarlandes, D--66041 Saarbrucken, Germany

Summary: We develop standard models for commuting tuples of bounded linear operators on a Hilbert space under certain polynomial positivity conditions, generalizing the work of V.~Müller and F.-H.~Vasilescu in $\rm{[6]}$, $\rm{[14]}$. As a consequence of the model, we prove a von Neumann-type inequality for such tuples. Up to similarity, we obtain the existence of in a certain sense ``unitary'' dilations.

Keywords: Multivariable spectral theory, weighted multishifts, standard models, dilations, functional calculus

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