Geodesic
On orthogonal bases in $L$
Matematičeskie zametki, Tome 6 (1969) no. 6, pp. 749-758 
A. N. Slepchenko. On orthogonal bases in $L$. Matematičeskie zametki, Tome 6 (1969) no. 6, pp. 749-758. http://geodesic.mathdoc.fr/item/MZM_1969_6_6_a10/
@article{MZM_1969_6_6_a10,
     author = {A. N. Slepchenko},
     title = {On orthogonal bases in $L$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {749--758},
     year = {1969},
     volume = {6},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_6_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The existence of orthogonal bases in $L$ which are not bases in $L^2$ is proved.