Bhat B, V, Rajama and John Tiju Cherian: Real normal operators and Williamson’s normal form. In: Acta scientiarum mathematicarum, (85) 3-4. pp. 507-518. (2019)
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Abstract
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.
Item Type: | Article |
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Journal or Publication Title: | Acta scientiarum mathematicarum |
Date: | 2019 |
Volume: | 85 |
Number: | 3-4 |
ISSN: | 2064-8316 |
Page Range: | pp. 507-518 |
Related URLs: | http://acta.bibl.u-szeged.hu/66425/ |
DOI: | 10.14232/actasm-018-570-5 |
Uncontrolled Keywords: | Spektrális tétel - normál operátor |
Additional Information: | Bibliogr.: p. 516-518. |
Date Deposited: | 2020. Apr. 23. 13:03 |
Last Modified: | 2021. Mar. 25. 15:34 |
URI: | http://acta.bibl.u-szeged.hu/id/eprint/66329 |
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