Geodesic
Certain numerical characteristics of $KN$-lineals
Matematičeskie zametki, Tome 14 (1973) no. 5, pp. 723-732.

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We study the properties of certain numerical characteristics in a normed lattice that characterize its conjugate space. A typical result is as follows: let $X$ be a $K_\sigma N$-space or a $KB$-lineal. If every sequence $\{x_n\}\subset X$ of pairwise disjoint positive elements with norms not exceedings 1 we have $$ \varliminf_{n\to\infty}\frac1n||x_1\vee x_2\vee\dots\vee x_n||=0, $$ then all the odd conjugate spaces $X^*, X^{***},\dots$ are $KB$-spaces. 
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     author = {Yu. A. Abramovich and G. Ya. Lozanovskii},
     title = {Certain numerical characteristics of $KN$-lineals},
     journal = {Matemati\v{c}eskie zametki},
     pages = {723--732},
     publisher = {mathdoc},
     volume = {14},
     number = {5},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_5_a12/}
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Yu. A. Abramovich; G. Ya. Lozanovskii. Certain numerical characteristics of $KN$-lineals. Matematičeskie zametki, Tome 14 (1973) no. 5, pp. 723-732. http://geodesic.mathdoc.fr/item/MZM_1973_14_5_a12/