Conjugations of Unitary operators, I

2024/02/22 by Mashreghi, Javad, Ptak, Marek, Ross, William T. · 1 citation
#47A465 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2402.14995

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 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 CUC = U^*.

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• C-self-adjoint contractive extensions of C-symmetric non-densely defined contractions

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