Power boundedness and similarity to contractions for some perturbations of isometries
Copyright policy )Power boundedness and similarity to contractions for some perturbations of isometries
Starting with the result of B. Sz.-Nagy about the similarity of some operators to a unitary one, a lot of specific results followed. In this paper, after a presentation of the main results of the first author's paper [``Generalized Toeplitz operators and similarity problems'' (Preprint IGD No. 30, Univ. Lyon 1, Villeurbanne) (1999; per bibl.); see also J. Oper. Theory 53, No. 1, 49--89 (2005; Zbl 1073.47010)] about power boundedness and similarity to a contraction, some applications of these results to one-dimensional perturbations of the shift operator are investigated. The paper has ten sections, analysing from various points of view the problems of power boundedness and similarity to a contraction.
- Université Claude Bernard Lyon 1 France
- Université Claude Bernard - Lyon 1 France
- Claude Bernard University Lyon 1 France
- Claude Bernard University Lyon 1 France
- Romanian Academy Romania
Structure theory of linear operators, power boundedness, Applied Mathematics, Blaschke products, etc., perturbations of isometries, similarity to contractions, \(H^p\)-classes, Analysis, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Real rational functions
Structure theory of linear operators, power boundedness, Applied Mathematics, Blaschke products, etc., perturbations of isometries, similarity to contractions, \(H^p\)-classes, Analysis, Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.), Real rational functions
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