A strict Positivstellensatz for the Weyl algebra

DOI10.1007/s00208-004-0604-4zbMath1137.47030arXivmath/0403076OpenAlexW2155263740MaRDI QIDQ1772092

Konrad Schmüdgen

Publication date: 15 April 2005

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0403076

zbMATH Keywords

Weyl algebraStone-von Neumann theorem\(^*\)-representation\(m\)-admissible wedgealgebraically bounded part of a \(^*\)-algebraFock-Bergman realizationHermitean element

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Algebras of unbounded operators; partial algebras of operators (47L60) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Semialgebraic sets and related spaces (14P10) Rings of differential operators (associative algebraic aspects) (16S32) Representations of (nonselfadjoint) operator algebras (47L55) Linear operators in ({}^*)-algebras (47C10)

Related Items (19)

Bounded elements of C\(^\ast\)-inductive locally convex spaces ⋮ Symmetry reduction of states. II: A non-commutative positivstellensatz for \(\mathbb{C} \mathbb{P}^n\) ⋮ A real nullstellensatz for free modules ⋮ Symmetry reduction of states. I ⋮ Positivstellensätze for algebras of matrices ⋮ A paradox in bosonic energy computations via semidefinite programming relaxations ⋮ Locally convex quasi \(^*\)-algebras with sufficiently many \(^*\)-representations ⋮ On the positivstellensatz in Weyl’s algebra ⋮ Some positivstellensätze for polynomial matrices ⋮ Maximal quadratic modules on \(*\)-rings. ⋮ A nichtnegativstellensatz for polynomials in noncommuting variables ⋮ A method for computing lowest eigenvalues of symmetric polynomial differential operators by semidefinite programming ⋮ Algebras of fractions and strict Positivstellensätze for ∗-algebras ⋮ A strict Positivstellensatz for enveloping algebras ⋮ Convexity and Semidefinite Programming in Dimension-Free Matrix Unknowns ⋮ SDP Relaxations for Non-Commutative Polynomial Optimization ⋮ Equivalence of order and algebraic properties in ordered \(^*\)-algebras ⋮ Positivstellensätze for polynomial matrices ⋮ On 𝑞-normal operators and the quantum complex plane

Cites Work

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• The \(K\)-moment problem for compact semi-algebraic sets
• Solving moment problems by dimensional extension
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• Uniform denominators in Hilbert's seventeenth problem
• Ordered linear spaces
• The quantum problem of moments. I
• Distinguished representations of strictly positive polynomials
• Extending the Archimedean Positivstellensatz to the Non-Compact Case
• n-Positivity of Unbounded *-Representations
• Harmonic Analysis in Phase Space. (AM-122)
• ^*-Orderings on a ring with involution
• Sur les algèbres de Weyl

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