Flat extensions in *-algebras

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.