The Banach--Saks index
Sbornik. Mathematics, Tome 195 (2004) no. 2, pp. 263-285

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The properties of the Banach–Saks index are studied in the class of rearrangement invariant spaces. The Banach–Saks indices of the spaces $L_{p,q}$ and some Orlicz spaces are calculated. Generalizations of the Banach–Saks theorems are obtained.
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     author = {E. M. Semenov and F. A. Sukochev},
     title = {The {Banach--Saks} index},
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E. M. Semenov; F. A. Sukochev. The Banach--Saks index. Sbornik. Mathematics, Tome 195 (2004) no. 2, pp. 263-285. http://geodesic.mathdoc.fr/item/SM_2004_195_2_a4/