Geodesic
An Analog of the Cameron--Johnson Theorem for Linear $\mathbb C$-Analytic Equations in Hilbert Space
Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 935-938

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The well-known Cameron–Johnson theorem asserts that the equation $\dot x=\mathcal A(t)x$ with a recurrent (Bohr almost periodic) matrix $\mathcal A(t)$ can be reduced by a Lyapunov transformation to the equation $\dot y=\mathcal B(t)y$ with a skew-symmetric matrix $\mathcal B(t)$, provided that all solutions of the equation $\dot x=\mathcal A(t)x$ and of all its limit equations are bounded on the whole line. In the note, a generalization of this result to linear $\mathbb C$-analytic equations in a Hilbert space is presented. 
@article{MZM_2000_68_6_a13,
     author = {D. N. Cheban},
     title = {An {Analog} of the {Cameron--Johnson} {Theorem} for {Linear} $\mathbb C${-Analytic} {Equations} in {Hilbert} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {935--938},
     publisher = {mathdoc},
     volume = {68},
     number = {6},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2000_68_6_a13/}
}
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D. N. Cheban. An Analog of the Cameron--Johnson Theorem for Linear $\mathbb C$-Analytic Equations in Hilbert Space. Matematičeskie zametki, Tome 68 (2000) no. 6, pp. 935-938. http://geodesic.mathdoc.fr/item/MZM_2000_68_6_a13/