HARNACK parts of ρ-Contractions

Gilles Cassier (1) , Mohammed Benharrat (2) , Soumia Belmouhoub

1 EDPA - Équations aux dérivées partielles, analyse
2 ENP - École nationale polytechnique [Alger, Algérie]

The purpose of this paper is to describe the Harnack parts for the operators of class C ρ (ρ > 0) on Hilbert spaces which were introduced by B. Sz. Nagy and C. Foias in [25]. More precisely, we study Harnack parts of operators with ρ-numerical radius one. The case of operators with ρ-numerical radius strictly less than 1 was described in [10]. We obtain a general criterion for compact ρ-contractions to be in the same Harnack part. We give a useful equivalent form of this criterion for usual contractions. Operators with numerical radius one received also a particular attention. Moreover, we study many properties of Harnack equivalence in the general case.

Mots clés: numerical range.; operator radii; ρ-contractions; Harnack parts; operator kernel

Domaines: Analyse fonctionnelle [math.FA]

Gilles Cassier, Mohammed Benharrat, Soumia Belmouhoub. HARNACK parts of ρ-Contractions. Journal of Operator Theory, 2018, Volume 80 (Issue 2), pp.453-480. ⟨hal-01417360v2⟩