Geodesic
Condition of conjugacy of $WCG$-spaces
Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 281-284 
A. N. Plichko. Condition of conjugacy of $WCG$-spaces. Matematičeskie zametki, Tome 23 (1978) no. 2, pp. 281-284. http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a11/
@article{MZM_1978_23_2_a11,
     author = {A. N. Plichko},
     title = {Condition of conjugacy of $WCG$-spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {281--284},
     year = {1978},
     volume = {23},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_2_a11/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that a $WCG$-space $E$ is conjugate to a Banach space if and only if its conjugate space $E'$ contains a norm-closed total subspace $M$, consisting of functionals which attain supremum on the unit sphere. Moreover, $M'=E$ in the duality established between $E$ and Eprime. An example, showing that this statement is in general not true for an arbitrary Banach space, is given.