On the shift index of contractions
In [9] the shift index K(T) of a contraction T acting on a Hilbert space is defined: /c(T) is the supremum of n such that Sn can be injected into T, where Sn is the unilateral shift of multiplicity n. In [11] the following question is posed: if T is a Cio-contraction and its unitary asymptote is a r...
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. 1-2 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16433 |
| Tartalmi kivonat: | In [9] the shift index K(T) of a contraction T acting on a Hilbert space is defined: /c(T) is the supremum of n such that Sn can be injected into T, where Sn is the unilateral shift of multiplicity n. In [11] the following question is posed: if T is a Cio-contraction and its unitary asymptote is a reductive unitary operator, then K(T) = oo? In this paper, a positive answer to this question is given. A combination of the answer to this question with results of [11] gives that, for a Cio-contraction T, k(T) < oo if and only if T is a quasiaffine transform of Sn for some finite n. |
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| Terjedelem/Fizikai jellemzők: | 279-290 |
| ISSN: | 0001-6969 |