Preservers of isometries
Let γ be a unimodular complex number, and let k be an integer. Then γAk is an isometry for any isometry A of a complex Banach space. It is shown that if f is an analytic function on the unit circle sending an isometry to an isometry for any norm, then f has the form z 7→ γzk for some unimodular γ an...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2018
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| Sorozat: | Acta scientiarum mathematicarum
84 No. 1-2 |
| Kulcsszavak: | Izometria |
| Online Access: | http://acta.bibl.u-szeged.hu/55800 |
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| 100 | 1 | |a Ilišević Dijana | |
| 245 | 1 | 0 | |a Preservers of isometries |h [elektronikus dokumentum] / |c Ilišević Dijana |
| 260 | |c 2018 | ||
| 300 | |a 3-17 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 84 No. 1-2 | |
| 520 | 3 | |a Let γ be a unimodular complex number, and let k be an integer. Then γAk is an isometry for any isometry A of a complex Banach space. It is shown that if f is an analytic function on the unit circle sending an isometry to an isometry for any norm, then f has the form z 7→ γzk for some unimodular γ and integer k. The same conclusion on f can be deduced if f is merely continuous and preserves the isometries of some special classes of norms on a fixed finite-dimensional complex Banach space. The result is extended to real Banach spaces X with dim X ≥ 4, and it is shown that one cannot get the same conclusion on f if dim X < 4. Further extensions of these results are also considered. | |
| 695 | |a Izometria | ||
| 700 | 0 | 1 | |a Kuzma Bojan |e aut |
| 700 | 0 | 1 | |a Li Chi-Kwong |e aut |
| 700 | 0 | 1 | |a Poon Edward |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/55800/1/math_084_numb_001-002_003-017.pdf |z Dokumentum-elérés |