1. Archimedean operator-theoretic Positivstellensätze
- Author
-
Jaka Cimpric
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,Operator algebra ,Real algebraic geometry ,Moment problems ,Operator (physics) ,Mathematics::Optimization and Control ,Extension (predicate logic) ,Operator algebras ,Hermitian matrix ,Analysis ,Mathematics - 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 positivstellensatze 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.
- Full Text
- View/download PDF