Real normal operators and Williamson’s normal form
A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose (adjoint). Astructure theorem for invertible skew-symmetric operators, which is analogous to the finite-dimensional situation, is also proved using elementary techn...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 3-4 |
| Kulcsszavak: | Spektrális tétel - normál operátor |
| doi: | 10.14232/actasm-018-570-5 |
| Online Access: | http://acta.bibl.u-szeged.hu/66329 |
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| 024 | 7 | |a 10.14232/actasm-018-570-5 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a zxx | ||
| 100 | 1 | |a Bhat B, V, Rajama | |
| 245 | 1 | 0 | |a Real normal operators and Williamson’s normal form |h [elektronikus dokumentum] / |c Bhat B, V, Rajama |
| 260 | |c 2019 | ||
| 300 | |a 507-518 | ||
| 490 | 0 | |a Acta scientiarum mathematicarum |v 85 No. 3-4 | |
| 520 | 3 | |a A simple proof is provided to show that any bounded normal operator on a real Hilbert space is orthogonally equivalent to its transpose (adjoint). Astructure theorem for invertible skew-symmetric operators, which is analogous to the finite-dimensional situation, is also proved using elementary techniques. The second result is used to establish the main theorem of this article, which is a generalization of Williamson’s normal form for bounded positive operators on infinite-dimensional separable Hilbert spaces. This has applications in the study of infinite mode Gaussian states. | |
| 695 | |a Spektrális tétel - normál operátor | ||
| 700 | 0 | 1 | |a John Tiju Cherian |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/66329/1/math_085_numb_003-004_507-518.pdf |z Dokumentum-elérés |