Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 2, 2003, pp. 299–314
DOI: 10.4171/ZAA/1147

Operator-Theoretic Positivstellensätze

C.-G. Ambrozie (1) and F.-H. Vasilescu (2)

(1) Institute of Mathematics, Romanian Academy, P.O. Box 1-764, 70700, BUCHAREST, ROMANIA
(2) U.F.R. de Mathématiques, Université Lille I, 59655, VILLENEUVE D'ASCQ CEDEX, FRANCE

We study the structure of positive polynomials with coefficients in an operator algebra as a non-commutative infinite-dimensional analogue of Hilbert's 17-th problem.

Keywords: Operator positivity, polynomials, semialgebraic sets