Archimedean operator-theoretic Positivstellens\"atze
Algebraic Geometry
2013-01-07 v2 Functional Analysis
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 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.
Cite
@article{arxiv.1011.4931,
title = {Archimedean operator-theoretic Positivstellens\"atze},
author = {Jaka Cimpric},
journal= {arXiv preprint arXiv:1011.4931},
year = {2013}
}
Comments
17 pages, revised version, to appear in the Journal of Functional Analysis