Conjugations of unitary operators, I

If U is a unitary operator on a separable complex Hilbert space H , an application of the spectral theorem says there is a conjugation C on H (an antilinear, involutive, isometry on H ) for which C U C = U ∗ . In this paper, we fix a unitary operator U and describe all of the conjugations C which sa...

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Bibliographic Details
Published in:Analysis and mathematical physics 2024, Vol.14 (3), p.62, Article 62
Main Authors: Mashreghi, Javad, Ptak, Marek, Ross, William T.
Format: Article
Language:English
Subjects:
Analysis
Conjugation
Hilbert space
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
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Summary:If U is a unitary operator on a separable complex Hilbert space H , an application of the spectral theorem says there is a conjugation C on H (an antilinear, involutive, isometry on H ) for which C U C = U ∗ . In this paper, we fix a unitary operator U and describe all of the conjugations C which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for U if and only if it is invariant for any conjugation C for which C U C = U ∗ .
ISSN:1664-2368
1664-235X
1664-235X
DOI:10.1007/s13324-024-00924-z