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Pure states, nonnegative polynomials and sums of squares

Publikationsart Peer-reviewed
Publikationsform Originalbeitrag (peer-reviewed)
Publikationsdatum 2012
Projekt Groupes sofiques: algèbre, analyse et dynamique
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Originalbeitrag (peer-reviewed)

Zeitschrift Commentarii Mathematici Helvetici
Volume (Issue) 87(1)
Seite(n) 113 - 140
Titel der Proceedings Commentarii Mathematici Helvetici


In recent years, much work has been devoted to a system- atic study of polynomial identities certifying strict or non-strict posi- tivity of a polynomial f on a basic closed set K ⊂ Rn. The interest in such identities originates not least from their importance in polyno- mial optimization. The majority of the important results requires the archimedean condition, which implies that K has to be compact. This paper introduces the technique of pure states into commutative algebra. We show that this technique allows an approach to most of the recent archimedean Stellens atze that is considerably easier and more concep- tual than the previous proofs. In particular, we reprove and strengthen some of the most important results from the last years. In addition, we establish several such results which are entirely new. They are the first that allow f to have arbitrary, not necessarily discrete, zeros in K.