Essential spherical isometries
A theorem of Fillmore, Stampfli and Williams asserts that a bounded linear Hilbert space operator is an essential isometry if and only if it is a compact perturbation of either an isometry or a coisometry with finite-dimensional kernel. In this note, we discuss the spherical analog of this result. I...
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| Dokumentumtípus: | Cikk |
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2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 3-4 |
| Kulcsszavak: | Hilbert-tér, Fillmore, Stampfli és Williams tétel, izometria |
| doi: | 10.14232/actasm-018-335-6 |
| Online Access: | http://acta.bibl.u-szeged.hu/66334 |
| Tartalmi kivonat: | A theorem of Fillmore, Stampfli and Williams asserts that a bounded linear Hilbert space operator is an essential isometry if and only if it is a compact perturbation of either an isometry or a coisometry with finite-dimensional kernel. In this note, we discuss the spherical analog of this result. It turns out that the spherical analog of this result does not hold verbatim, and this failuremay be attributed to the fact that in dimension d>2, there exist spherical isometries with finite-dimensional joint cokernel, which are not essential spher-ical unitaries. We also discuss some strictly higher-dimensional obstructions in representing an essential spherical isometry as a compact perturbation of aspherical isometry. |
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| Terjedelem/Fizikai jellemzők: | 589-594 |
| ISSN: | 2064-8316 |