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. 2024;14(3):62.
doi: 10.1007/s13324-024-00924-z. Epub 2024 May 16.

Conjugations of unitary operators, I

Javad Mashreghi  1 , Marek Ptak  2 , William T Ross  3
Affiliations

Conjugations of unitary operators, I

Javad Mashreghi et al. Anal Math Phys. 2024.

Abstract

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 CUC=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 CUC=U∗.

Keywords: Complex symmetric operators; Unitary operators.

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