Geodesic
Completely linear functionals in partially ordered spaces
Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 187-195

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For an arbitrary normed space $X$ the set $(X^{**})^\pi$ in $X^{**}$ introduced. It is proved that if $X$ is a $KN$-lineal then $\overline{X}^*=(X^{**})^\pi$, where $\overline{X}^*$ is the Nakano dual to the Banach dual $X^*$. By the same token $\overline{X}^*$ is not in any way related with any partial ordering in the $KN$-lineal $X$. 
@article{MZM_1970_8_2_a6,
     author = {G. Ya. Lozanovskii},
     title = {Completely linear functionals in partially ordered spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {187--195},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a6/}
}
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G. Ya. Lozanovskii. Completely linear functionals in partially ordered spaces. Matematičeskie zametki, Tome 8 (1970) no. 2, pp. 187-195. http://geodesic.mathdoc.fr/item/MZM_1970_8_2_a6/