Geodesic
Generalized elements of best approximation
Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 513-523.

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It is proved that generalized elements of best approximation (GEBA's) are approximated by minimizing nets in the $\sigma(X^{**},X^*)$ topology. Criteria for GEBA's are established. GEBA's are considered in $\Gamma^*$ where $\Gamma$ is a 1-normalizing subspace of $X^*$. 
@article{MZM_1976_19_4_a3,
     author = {L. P. Vlasov},
     title = {Generalized elements of best approximation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {513--523},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a3/}
}
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L. P. Vlasov. Generalized elements of best approximation. Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 513-523. http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a3/