Flat extensions in *-algebras
Bernard Mourrain (INRIA Sophia Antipolis), Konrad Schm\"udgen

TL;DR
This paper proves a flat extension theorem for positive linear functionals on *-algebras and applies it to various moment problems involving polynomials, matrices, and Lie algebra enveloping algebras.
Contribution
Introduces a flat extension theorem for *-algebras and demonstrates its application to solve truncated moment problems in different algebraic contexts.
Findings
Established a flat extension theorem for positive linear functionals.
Applied the theorem to truncated moment problems on cylinder sets.
Extended the approach to matrices of polynomials and Lie algebra enveloping algebras.
Abstract
The main result of the paper is a flat extension theorem for positive linear functionals on *-algebras. The theorem is applied to truncated moment problems on cylinder sets, on matrices of polynomials and on enveloping algebras of Lie algebras.
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Taxonomy
TopicsMatrix Theory and Algorithms · Numerical methods for differential equations · Stability and Control of Uncertain Systems
