On power bounded operators with holomorphic eigenvectors II.

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 cons...

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Elmentve itt :
Bibliográfiai részletek
Szerző: Gamal Maria F.
Dokumentumtípus: Cikk
Megjelent: Bolyai Institute, University of Szeged Szeged 2020
Sorozat:Acta scientiarum mathematicarum 86 No. 3-4
Kulcsszavak:Matematika
Tárgyszavak:
doi:10.14232/actasm-020-283-1

Online Access:http://acta.bibl.u-szeged.hu/73903
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245 1 3 |a On power bounded operators with holomorphic eigenvectors II.  |h [elektronikus dokumentum] /  |c  Gamal Maria F. 
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490 0 |a Acta scientiarum mathematicarum  |v 86 No. 3-4 
520 3 |a 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. 
650 4 |a Természettudományok 
650 4 |a Matematika 
695 |a Matematika 
856 4 0 |u http://acta.bibl.u-szeged.hu/73903/1/math_086_numb_003-004_549-562.pdf  |z Dokumentum-elérés