Geodesic
Moduli of Hankel operators and a problem of V. V. Peller and S. V. Khrushchev
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIV, Tome 141 (1985), pp. 39-55 
S. R. Treil'. Moduli of Hankel operators and a problem of V. V. Peller and S. V. Khrushchev. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIV, Tome 141 (1985), pp. 39-55. http://geodesic.mathdoc.fr/item/ZNSL_1985_141_a2/
@article{ZNSL_1985_141_a2,
     author = {S. R. Treil'},
     title = {Moduli of {Hankel} operators and a~problem of {V.} {V.} {Peller} and {S.} {V.} {Khrushchev}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {39--55},
     year = {1985},
     volume = {141},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_141_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Theorem. {\it Let $A$ be a bounded nonnegativ, selfadjoint operator such that $0\in\sigma(A)$, $\dim\operatorname{Ker}A=0$ or $\infty$, the operator $A|(\operatorname{Ker}A)^\bot$ is unitary equivalent to the operator of multiplication by $x$ in the space $L^2(\mu)$, where $\mu$ is the discrete measure. Then there exists a Hankel operator $H_\varphi$ such that the operator $A$ is unitarily equivalent to the operator $(H_\varphi^*H_\varphi)^{1/2}$.}