Essential spherical isometries
A result due to Williams, Stampfli and Fillmore shows that an essential isometry T on a Hilbert space H is a compact perturbation of an isometry if and only if ind(T) ≤ 0. A recent result of S. Chavan yields an analogous characterization of essential spherical isometries T = (T1, . . . , Tn) ∈ B(H)...
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| Dokumentumtípus: | Cikk |
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2020
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| Sorozat: | Acta scientiarum mathematicarum
86 No. 3-4 |
| Kulcsszavak: | Hilbert-tér, Fillmore, Stampfli és Williams tétel, Izometria |
| doi: | 10.14232/actasm-020-767-3 |
| Online Access: | http://acta.bibl.u-szeged.hu/73909 |
| Tartalmi kivonat: | A result due to Williams, Stampfli and Fillmore shows that an essential isometry T on a Hilbert space H is a compact perturbation of an isometry if and only if ind(T) ≤ 0. A recent result of S. Chavan yields an analogous characterization of essential spherical isometries T = (T1, . . . , Tn) ∈ B(H) n with dim( Tn i=1 ker(Ti)) ≤ dim( Tn i=1 ker(T i )). In the present note we show that in dimension n > 1 the result of Chavan holds without any condition on the dimensions of the joint kernels of T and T. |
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| Terjedelem/Fizikai jellemzők: | 667-670 |
| ISSN: | 2064-8316 |