A nonhypercyclic operator with orbit-density properties
In this note we construct an operator T on a (separable, complex) Hilbert space such that for every nonzero vector x, the sequence {||Tnx||}ngN is dense in R+, but despite this, T is not hypercyclic (i.e., no vector in H has a dense orbit). In addition, this operator has the property that there are...
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/16268 |
| Tartalmi kivonat: | In this note we construct an operator T on a (separable, complex) Hilbert space such that for every nonzero vector x, the sequence {||Tnx||}ngN is dense in R+, but despite this, T is not hypercyclic (i.e., no vector in H has a dense orbit). In addition, this operator has the property that there are subsequences {r n } and {qn} of N such that Trn —> 0 and TQn —> +oo (properly defined) in the strong operator topology. Finally, neither T nor T* has point spectrum. This partially answers a question in [5] and provides a counterexample to some reasonable conjectures. |
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| Terjedelem/Fizikai jellemzők: | 743-756 |
| ISSN: | 0001-6969 |