On the set of upper bounds for a finite family of self-adjoint operators

Gilles Cassier (1) , Mohand Ould Ali (2)

1 EDPA - Équations aux dérivées partielles, analyse
2 Equipe d'Analyse

We study the structure and properties of the weak closed set of all upper bounds of a finite family of self-adjoint operators for Löwner ordering. Firstly, we prove that we can find a upper bound satisfying additional constraints. Secondly, we give two characterizations of minimal upper bounds. Finally, we furnish a complete description of pairs of positives operators such that the sum is a minimal upper bound.

Mots clés: Self-adjoint operators; minimal upper bounds; Löwner ordering; minimal upper bounds.

Domaines: Analyse fonctionnelle [math.FA]

Gilles Cassier, Mohand Ould Ali. On the set of upper bounds for a finite family of self-adjoint operators. Theta,Bucharest. 25th International Conference on Operator Theory, Jun 2014, Timisoara, Romania. 18, pp.1-14, 2016, Theta Series in Advanced Mathematics. ⟨hal-00980617⟩