Gamal Maria F.: On power bounded operators with holomorphic eigenvectors II. In: Acta scientiarum mathematicarum, (86) 3-4. pp. 549-562. (2020)
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Absztrakt (kivonat)
In [U] (among other results), M. Uchiyama gave necessary and sufficient conditions for contractions to be similar to the unilateral shift S of multiplicity 1 in terms of norm-estimates of complete analytic families of eigenvectors of their adjoints. In [Gam2], a cyclic power bounded operator is constructed which has the requested norm-estimates, is a quasiaffine transform of S, but is not quasisimilar to S. In this paper, a power bounded operator is constructed which has the requested norm-estimates, is quasisimilar to S, but is not similar to S. The question whether the criterion for contractions to be similar to S can be generalized to polynomially bounded operators remains open. Also, for every cardinal number 2 ≤ N ≤ ∞, a power bounded operator T is constructed such that T is a quasiaffine transform of S and dim ker T ∗ = N. This is impossible for polynomially bounded operators. Moreover, the constructed operators T have the requested norm-estimates of complete analytic families of eigenvectors of T.
Mű típusa: | Cikk, tanulmány, mű |
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Rovatcím: | Analysis |
Befoglaló folyóirat/kiadvány címe: | Acta scientiarum mathematicarum |
Dátum: | 2020 |
Kötet: | 86 |
Szám: | 3-4 |
ISSN: | 2064-8316 |
Oldalak: | pp. 549-562 |
Nyelv: | angol |
Befoglaló mű URL: | http://acta.bibl.u-szeged.hu/73790/ |
DOI: | 10.14232/actasm-020-283-1 |
Kulcsszavak: | Matematika |
Megjegyzések: | Bibliogr.: p. 561-562. ; összefoglalás angol nyelven |
Feltöltés dátuma: | 2021. nov. 15. 13:52 |
Utolsó módosítás: | 2021. nov. 15. 13:52 |
URI: | http://acta.bibl.u-szeged.hu/id/eprint/73903 |
Tétel nézet |