Examples of cyclic polynomially bounded operators that are not similar to contractions

Gamal Maria F.: Examples of cyclic polynomially bounded operators that are not similar to contractions. In: Acta scientiarum mathematicarum, (82) 3-4. pp. 597-628. (2016)

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Abstract

The question if a polynomially bounded operator is similar to a contraction was posed by Halmos and was answered in the negative by Pisier. His counterexample is an operator of infinite multiplicity, while all its restrictions on invariant subspaces of finite multiplicity are similar to contractions. In the paper, cyclic polynomially bounded operators which are not similar to contractions and are quasisimilar to Co-contractions or to isometries are constructed. The construction is based on a perturbation of the sequence of finite dimensional operators which is uniformly polynomially bounded, but is not uniformly completely polynomially bounded, constructed by Pisier.

Item Type:	Article
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2016
Volume:	82
Number:	3-4
ISBN:	0001-6969
Page Range:	pp. 597-628
Language:	English
Publisher:	Bolyai Institute, University of Szeged
Place of Publication:	Szeged
Official URL:	http://www.acta.hu
Related URLs:	http://acta.bibl.u-szeged.hu/45435/
DOI:	10.14232/actasm-016-016-4
Uncontrolled Keywords:	Polinomiális korlátos operátor, Matematika
Additional Information:	Bibliogr.: p. 627-628. ; összefoglalás angol nyelven
Subjects:	01. Natural sciences 01. Natural sciences > 01.01. Mathematics
Date Deposited:	2017. Apr. 07. 11:02
Last Modified:	2026. Feb. 24. 09:01
URI:	http://acta.bibl.u-szeged.hu/id/eprint/46329

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