Flat extensions in ∗-algebras

Bernard Mourrain (1) , Konrad Schmüdgen (2)

1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
2 Mathematisches Institut

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.

Mots clés: ∗-algebras; flat extension; hermitian linear form; enveloping algebra; truncated moment problem; GNS construction

Domaines: Géométrie algébrique [math.AG]

Bernard Mourrain, Konrad Schmüdgen. Flat extensions in ∗-algebras. Proceedings of the American Mathematical Society, 2016, 144 (11), pp.4873-4885. ⟨10.1090/proc/13158⟩. ⟨hal-01009909⟩