Journal of Operator Theory

Volume 56, Issue 2, Fall 2006 pp. 273-290.

Denominateurs universels pour la decomposition de polynomes positifs sur un espace de Hilbert

Authors: O. Demanze (1) and A. Mouze (2)
Author institution: (1) Laboratoire de Mathematiques, UMR 8524, Universite Lille 1, Villeneuve d'Ascq, 59650, France
(2) Laboratoire de Mathematiques, UMR 8524, Ecole Centrale de Lille, Villeneuve d'Ascq, 59650, France

Summary: In this work, we prove that, under natural conditions, one can give representations of positive polynomials defined on a Hilbert space ${\mathcal H}$ where appear squares of rational fractions with specified denominators and the norm of powers of $S^*$ (where $S$ is the unilateral shift on ${\mathcal H}$). We generalize some recent results using functional analysis methods in finite dimensional case.

Keywords: Polynomial representation, semialgebraic sets, positive polynomials, sums of squares.

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