On contractions that are quasiaffine transforms of unilateral shifts
It is known that if T is a contraction of class Cio and / — T*T is of trace class, then T is a quasiaffine transform of a unilateral shift. Also it is known that if the multiplicity of a unilateral shift is infinite, the converse is not true. In this paper the converse for a finite multiplicity is p...
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/16269 |
| Tartalmi kivonat: | It is known that if T is a contraction of class Cio and / — T*T is of trace class, then T is a quasiaffine transform of a unilateral shift. Also it is known that if the multiplicity of a unilateral shift is infinite, the converse is not true. In this paper the converse for a finite multiplicity is proved: if T is a contraction and T is a quasiaffine transform of a unilateral shift of finite multiplicity, then I — T*T is of trace class. As a consequence we obtain that if a contraction T has finite multiplicity and its characteristic function has an outer left scalar multiple, then / — T*T is of trace class. |
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| Terjedelem/Fizikai jellemzők: | 757-767 |
| ISSN: | 0001-6969 |