Weak orbit-transitivity on Hilbert space
This note is concerned with weakly hypercyclic vectors and operators and weakly orbit-transitive operators (definitions below). We show that, given a sequence {xn} of vectors with ||a:n|| —» oo and 0 £ {xn}~, there exists another sequence {wn} with approximately equal growth rate that is weakly dens...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2010
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| Sorozat: | Acta scientiarum mathematicarum
76 No. 1-2 |
| Kulcsszavak: | Matematika, Hilbert-tér |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16342 |
| Tartalmi kivonat: | This note is concerned with weakly hypercyclic vectors and operators and weakly orbit-transitive operators (definitions below). We show that, given a sequence {xn} of vectors with ||a:n|| —» oo and 0 £ {xn}~, there exists another sequence {wn} with approximately equal growth rate that is weakly dense. This complements a result of V. Kadets [11]. Then we apply Kadets' theorem, together with others used previously [10], to show that certain classes of operators consist entirely of non-weakly-orbit-transitive operators, thereby generalizing the results of [10]. Along the way we show that K. Ball's complex-plank theorem [2] is equivalent to a (slightly stronger) version of an old theorem of Beauzamy. |
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| Terjedelem/Fizikai jellemzők: | 155-164 |
| ISSN: | 0001-6969 |