Archimedean operator-theoretic Positivstellensätze |
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Authors: | J Cimpri? |
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Institution: | University of Ljubljana, Faculty of Math. and Phys., Dept. of Math., Jadranska 19, SI-1000 Ljubljana, Slovenia |
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Abstract: | 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 positivstellensätze 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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Keywords: | Real algebraic geometry Operator algebras Moment problems |
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