Geodesic
The Adamyan–Arov–Krein theorem: Vectorial variant
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIV, Tome 141 (1985), pp. 56-71 
S. R. Treil. The Adamyan–Arov–Krein theorem: Vectorial variant. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIV, Tome 141 (1985), pp. 56-71. http://geodesic.mathdoc.fr/item/ZNSL_1985_141_a3/
@article{ZNSL_1985_141_a3,
     author = {S. R. Treil},
     title = {The {Adamyan{\textendash}Arov{\textendash}Krein} theorem: {Vectorial} variant},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {56--71},
     year = {1985},
     volume = {141},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_141_a3/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

One obtains the following description of the $s$–numbers of the vectorial Hankel operators $H_{\varphi}$, $\varphi\in L^{\infty}(E_1,E_2)$. Theorem 1. {\it $s_n(H_{\varphi})=\inf\{\|H_{\varphi}-H_{\psi}\|:\operatorname{rank} H_{\psi}\le n\}$}. The theorem generalizes the known Adamyan–Arov–Krein result and in the case $\min(\dim E_1,\dim E_2)<\infty$ has been proved by Ball and Helton. One obtains a constructive description of the Hankel operators of finite rank and one gives a formula for the rank of such an operator.