Revista Matemática Iberoamericana

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Volume 33, Issue 2, 2017, pp. 469–488
DOI: 10.4171/RMI/945

Classes of contractions and Harnack domination

Catalin Badea[1], Laurian Suciu[2] and Dan Timotin[3]

(1) Laboratoire Paul Painlevé, UMR CNRS 8524, Université Lille 1, Bâtiment M2, 59655, VILLENEUVE D'ASCQ CEDEX, FRANCE
(2) Department of Mathematics and Informatics, “Lucian Blaga” University of Sibiu, Dr. Ion Ratiu 5-7, 550012, SIBIU, ROMANIA
(3) Institute of Mathematics “Simion Stoilow”, Romanian Academy, P.O. Box 1-764, 014700, BUCHAREST, ROMANIA

Several properties of the Harnack domination of linear operators acting on Hilbert space with norm less or equal than one are studied. Thus, the maximal elements for this relation are identified as precisely the singular unitary operators, while the minimal elements are shown to be the isometries and the adjoints of isometries. We also show how a large range of properties (e.g., convergence of iterates, peripheral spectrum, ergodic properties) are transfered from a contraction to one that Harnack dominates it.

Keywords: Harnack domination, resolvent, unitary operators, convergence of iterates, ergodic properties

Badea Catalin, Suciu Laurian, Timotin Dan: Classes of contractions and Harnack domination. Rev. Mat. Iberoamericana 33 (2017), 469-488. doi: 10.4171/RMI/945