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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| Dokumentumtípus: | Cikk |
| Megjelent: |
2020
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| Sorozat: | Acta scientiarum mathematicarum
86 No. 3-4 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-020-283-1 |
| Online Access: | http://acta.bibl.u-szeged.hu/73903 |
| Tartalmi 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. |
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| Terjedelem/Fizikai jellemzők: | 549-562 |
| ISSN: | 2064-8316 |