HARNACK parts of $\rho$-Contractions
Functional Analysis
2016-12-20 v1
Abstract
The purpose of this paper is to describe the Harnack parts for the operators of class C ( \textgreater{} 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 -numerical radius one. The case of operators with -numerical radius strictly less than 1 was described in [10]. We obtain a general criterion for compact -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.
Keywords
Cite
@article{arxiv.1612.05763,
title = {HARNACK parts of $\rho$-Contractions},
author = {Gilles Cassier and Mohammed Benharrat and Soumia Belmouhoub},
journal= {arXiv preprint arXiv:1612.05763},
year = {2016}
}