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arXiv · 2402.14997

Conjugations of Unitary Operators, II

Javad Mashreghi·Marek Ptak·William T. Ross
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Abstract

For a given unitary operator $U$ on a separable complex Hilbert space $\h$, we describe the set $\mathscr{C}_{c}(U)$ of all conjugations $C$ (antilinear, isometric, and involutive maps) on $\h$ for which $C U C = U$. As this set might be empty, we also show that $\mathscr{C}_{c}(U) \not = \varnothing$ if and only if $U$ is unitarily equivalent to $U^{*}$.

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Javad Mashreghi, Marek Ptak, William T. Ross. 2024-02-22. Conjugations of Unitary Operators, II. https://arxiv.org/abs/2402.14997

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