Geodesic
About estimates of the $\mathscr{K}$-divisibility constant for Banach pairs
Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 2, pp. 179-191

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The paper contains some results on estimates of the $\mathscr{K}$-divisibility constant for Banach pairs. Its has been established that it is impossible to improve the estimate $3+2\sqrt2$ for any Banach pair and $4$ any pair of Banach lattices using the method of Yu. A. Brudnyi and N. Ya. Krugljak. I give a proof of Sedaev–Semenov theorem for the pair $(L_1^1,L_1)$ with measure on half-axis, using only the properties of concave functions. 
@article{DVMG_2013_13_2_a1,
     author = {A. A. Dmitriev},
     title = {About estimates of the $\mathscr{K}$-divisibility constant for {Banach} pairs},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {179--191},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2013_13_2_a1/}
}
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A. A. Dmitriev. About estimates of the $\mathscr{K}$-divisibility constant for Banach pairs. Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 2, pp. 179-191. http://geodesic.mathdoc.fr/item/DVMG_2013_13_2_a1/