Real normal operators and Williamson’s normal form

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
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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