Geodesic
Boundary values of a convergent sequence of J-contractive matrix-functions
Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 491-500 
D. Z. Arov; L. A. Simakova. Boundary values of a convergent sequence of J-contractive matrix-functions. Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 491-500. http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a1/
@article{MZM_1976_19_4_a1,
     author = {D. Z. Arov and L. A. Simakova},
     title = {Boundary values of a convergent sequence of {J-contractive} matrix-functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {491--500},
     year = {1976},
     volume = {19},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this note it is proved that if $W_n(z)$ are $J$-contractive matrix-functions which are meromorphic in the disk $|z|<1$ ($J-W_n^*(z)JW_n(z)\ge0$, $J^*=J$, $J^2=I$), $W_n(z)\to W(z)$, as $n\to\infty$, $$ W^*(z)JW(z)\le W_n^*(z)JW_n(z) $$ and $$ \det W(z)\not\equiv0, $$ then there exists a subsequence $W_{n_k}(z)$ whose boundary values $$ W^*_{n_k}(\zeta)JW_{n_k}(\zeta)\to W^*(\zeta)JW(\zeta)\quad (\text{a. e. }|\zeta|=1). $$ It follows from this result that every convergent Blaschke–Potapov product has $J$-unitary boundary values.