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. In: Acta scientiarum mathematicarum, (85) 1-2. pp. 313-323. (2019)

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Absztrakt (kivonat)

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.

Mű típusa:	Cikk, tanulmány, mű
Befoglaló folyóirat/kiadvány címe:	Acta scientiarum mathematicarum
Dátum:	2019
Kötet:	85
Szám:	1-2
ISSN:	2064-8316
Oldalak:	pp. 313-323
Hivatalos webcím (URL):	http://www.acta.hu
Befoglaló mű URL:	http://acta.bibl.u-szeged.hu/62105/
DOI:	10.14232/actasm-018-797-y
Kulcsszavak:	Matematika, Polinom, Operátor
Megjegyzések:	Bibliogr.: 323. p. ; összefoglalás angol nyelven
Feltöltés dátuma:	2019. szep. 25. 10:57
Utolsó módosítás:	2021. már. 25. 15:30
URI:	http://acta.bibl.u-szeged.hu/id/eprint/62149

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