Harnack and Shmul'yan pre-order relations for Hilbert space contractions

Catalin Badea (1, 2) , Laurian Suciu (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Université de Lille
3 Universitatea "Lucian Blaga" Sibiu

We study the behavior of some classes of Hilbert space contractions with respect to the Harnack and Shmul'yan pre-order relations. We also discuss the corresponding equivalence relations, as well as an extension, recently considered by S. ter Horst, of the Shmul'yan pre-order from contractions to the operator-valued Schur class of functions.

Mots clés: Harnack pre-order; Shmul'yan pre-order; Hilbert space contractions; asymptotic limit; quasi normal operators; partial isometries; Toeplitz operators

Domaines: Analyse fonctionnelle [math.FA]

Catalin Badea, Laurian Suciu. Harnack and Shmul'yan pre-order relations for Hilbert space contractions. 2015. ⟨hal-01232071⟩