Archimedean operator-theoretic Positivstellensätze

Details Archimedean operator-theoretic Positivstellensätze Archimedean operator-theoretic Positivstellensätze

2010-11-22

arxiv.org/abs/1011.4931v2

Mathematics

Algebraic Geometry

17 pages, revised version, to appear in the Journal of Functional Analysis

Scientific paper

We prove a general archimedean positivstellensatz for hermitian operator-valued polynomials and show that it implies the multivariate Fejer-Riesz Theorem of Dritschel-Rovnyak and positivstellens\"atze of Ambrozie-Vasilescu and Scherer-Hol. We also obtain several generalizations of these and related results. The proof of the main result depends on an extension of the abstract archimedean positivstellensatz for *-algebras that is interesting in its own right.

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