Universality of weighted composition operators on L2 ([0,1]) and Sobolev spaces
It is shown that a class of composition operators C$ has the property that for every A in the interior of the spectrum of C$ the operator U = Cj, — Aid is universal in the sense of Caradus, i.e., every Hilbert space operator has a non-zero multiple similar to the restriction of U to an invariant sub...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2012
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| Sorozat: | Acta scientiarum mathematicarum
78 No. 3-4 |
| Kulcsszavak: | Matematika, Szoboljev-tér, Operátorelmélet |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16452 |
| Tartalmi kivonat: | It is shown that a class of composition operators C$ has the property that for every A in the interior of the spectrum of C$ the operator U = Cj, — Aid is universal in the sense of Caradus, i.e., every Hilbert space operator has a non-zero multiple similar to the restriction of U to an invariant subspace. As a generalization, weighted composition operators on the L2 and Sobolev spaces of the unit interval are shown to have the same property and thus a complete knowledge of their minimal invariant subspaces would imply a solution to the invariant subspace problem for Hilbert space. Moreover, a generalization of sufficient conditions for an operator to be universal is obtained. Cyclicity and non-cyclicity results for a certain class of weights and composition functions are also proved. |
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| Terjedelem/Fizikai jellemzők: | 609-642 |
| ISSN: | 0001-6969 |