Conjugations of Unitary operators, I

Javad Mashreghi; Marek Ptak; William T. Ross

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arXiv · 2402.14995

Conjugations of Unitary operators, I

Javad Mashreghi·Marek Ptak·William T. Ross

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Abstract

If $U$ is a unitary operator on a separable complex Hilbert space $\mathcal{H}$, an application of the spectral theorem says there is a conjugation $C$ on $\mathcal{H}$ (an antilinear, involutive, isometry on $\mathcal{H}$) 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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BibTeX RIS

Javad Mashreghi, Marek Ptak, William T. Ross. 2024-02-22. Conjugations of Unitary operators, I. https://arxiv.org/abs/2402.14995

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