DOI
10.1007/s13324-024-00924-z
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*.
Document Type
Article
Publication Date
5-16-2024
Publisher Statement
Copyright © 2024, Springer Link.
DOI: https://doi.org/10.1007/s13324-024-00924-z
The definitive version is available at: https://link.springer.com/article/10.1007/s13324-024-00924-z
Recommended Citation
Mashreghi, J., Ptak, M. & Ross, W.T. "Conjugations of unitary operators, I. " Analysis and Mathematical Physics 14, 62 (2024): 1-31. doi:10.1007/s13324-024-00924-z