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

Gamal, Maria F.: Examples of cyclic polynomially bounded operators that are not similar to contractions, II. Acta scientiarum mathematicarum, (85) 1-2. pp. 313-323. (2019)

[img] Cikk, tanulmány, mű
math_085_numb_001-002_313-323.pdf
Hozzáférés joga: Campus

Download (201kB)

Abstract

The question if every 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 [G], cyclic polynomially bounded operators which are not similar to contractions were constructed. The construction was based on a perturbation of a sequence of finite-dimensional operators which is uniformly polynomially bounded, but is not uniformly completely polynomially bounded, studied earlier by Pisier. In this paper, a cyclic polynomially bounded operator T0 is constructed so that T0 is not similar to a contraction and ωa(T0) = O. Here ωa(z) = exp(a z+1 z−1 ), z ∈ D, a > 0, and D is the open unit disk. To obtain such a T0, a slight modification of the construction from [G] is needed.

Item Type: Article
Journal or Publication Title: Acta scientiarum mathematicarum
Date: 2019
Volume: 85
Number: 1-2
Page Range: pp. 313-323
ISSN: 2064-8316
DOI: https://doi.org/10.14232/actasm-018-797-y
Uncontrolled Keywords: Matematika, Polinom, Operátor
Additional Information: Bibliogr.: 323. p. ; összefoglalás angol nyelven
Official URL: http://www.acta.hu
Date Deposited: 2019. Sep. 25. 10:57
Last Modified: 2019. Sep. 25. 10:57
URI: http://acta.bibl.u-szeged.hu/id/eprint/62149

Actions (login required)

View Item View Item