Geodesic
Characteristic properties of strong integral and strong $B$-integral self-adjoint operators
Matematičeskie zametki, Tome 8 (1970) no. 5, pp. 653-661 
V. B. Korotkov. Characteristic properties of strong integral and strong $B$-integral self-adjoint operators. Matematičeskie zametki, Tome 8 (1970) no. 5, pp. 653-661. http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a12/
@article{MZM_1970_8_5_a12,
     author = {V. B. Korotkov},
     title = {Characteristic properties of strong integral and strong $B$-integral self-adjoint operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {653--661},
     year = {1970},
     volume = {8},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_5_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A proof that a strong integral (strong B-integral) self-adjoint operator in $L_2(a,\,b)$ is a Hilbert-Schmidt operator (a kernel operator).