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 |
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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 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 507-518 |
| ISSN: | 2064-8316 |