Abstract:
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.
Key words:Banach couple, interpolation of linear operators, $\mathscr{K}$-method, $\mathscr{K}$-functional, constant $\mathscr{K}$-divisibility.
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