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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.~M\"uller and F.-H.~Vasilescu in \cite{[6]}, \cite{[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.

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