Orthogonalization of Positive Operator Valued Measures

Mikael de la Salle (1, 2, 3)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 EDPA - Équations aux dérivées partielles, analyse
3 ICJ - Institut Camille Jordan

We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal partition of unity in the same von Neumann algebra. This generalizes to infinite dimension and slightly strengthens previous results in matrix algebras by Kempe-Vidick and Ji-Natarajan-Vidick-Wright-Yuen. We also generalize to infinite dimension a duality result between POVMs and minimal majorants of finite subsets in the predual of a von Neumann algebra.

Domaines: Analyse fonctionnelle [math.FA]; Théorie des groupes [math.GR]; Algèbres d'opérateurs [math.OA]

Mikael de la Salle. Orthogonalization of Positive Operator Valued Measures. Comptes Rendus. Mathématique, 2022, 360 (G5), pp.549-560. ⟨10.5802/crmath.326⟩. ⟨hal-03264860⟩