Hyperinvariant subspaces for Bishop-type operators
We present a self-contained method initiated by A. M. Davie to prove the existence of nontrivial hyperinvariant subspace for Bishop-type operator Ta on L2 (0,1) associated with an irrational a e (0,1). Using all the strength of the Denjoy-Carleman theorem, we prove that our method works except on a...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2008
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| Sorozat: | Acta scientiarum mathematicarum
74 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16265 |
| Tartalmi kivonat: | We present a self-contained method initiated by A. M. Davie to prove the existence of nontrivial hyperinvariant subspace for Bishop-type operator Ta on L2 (0,1) associated with an irrational a e (0,1). Using all the strength of the Denjoy-Carleman theorem, we prove that our method works except on a set of HausdorfF measure equal to zero. We also show how to construct Liouville numbers a for which Ta has nontrivial hyperinvariant subspaces. |
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| Terjedelem/Fizikai jellemzők: | 689-718 |
| ISSN: | 0001-6969 |