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Dal'nevost. Mat. Zh., 2013, Volume 13, Number 2, Pages 179–191 (Mi dvmg261)  

About estimates of the $\mathscr{K}$-divisibility constant for Banach pairs

A. A. Dmitriev

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok

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

Full text: PDF file (181 kB)
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UDC: 517.983.8
MSC: 46B70
Received: 21.05.2013

Citation: A. A. Dmitriev, “About estimates of the $\mathscr{K}$-divisibility constant for Banach pairs”, Dal'nevost. Mat. Zh., 13:2 (2013), 179–191

Citation in format AMSBIB
\Bibitem{Dmi13}
\by A.~A.~Dmitriev
\paper About estimates of the $\mathscr{K}$-divisibility constant for Banach pairs
\jour Dal'nevost. Mat. Zh.
\yr 2013
\vol 13
\issue 2
\pages 179--191
\mathnet{http://mi.mathnet.ru/dvmg261}


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