Far Eastern Mathematical Journal

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On estimate of the K-divisibility constant for Banach pairs


Dmitriev A. A.

2013, issue 2, Ń. 179-191


Abstract
The paper contains some results on estimates of the 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 $4$ for any pair of Banach lattices using the method of Yu. A. Brudnyi and N. Ya. Krugljak. The Sedaev-Semenov theorem for the pair $(L_1$1, L_1)$ with measure on half-axis has been proved by only the properties of concave functions.

Keywords:
Banach couple, interpolation of linear operators, K-method, K-functional, constant K-divisibility

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References

[1] Iu.A. Brudnyi, N. Ia.Krugliak, “Funktory veshchestvennoi interpoliatsii”, DAN SSSR, 256:1 (1981), 14–17.
[2] V. I. Ovchinnikov, The method of orbit in interpolation theory, Math. Rept., 1, Part 2, Harwood Acad. Publ., London, 1984.
[3] M. Cwikel, B. Jawerth, M. Milman, “On the fundamental lemma of interpolation theory”, J. Approx. Theory, 60:1 (1990), 70–82.
[4] A. A. Dmitriev, “O konstante K-delimosti funktsionala Petre pary banakhovykh reshetok”, DV shkola-seminar im. akad. E. V. Zolotova. Vladivostok, 27.08–02.09, Dal'nauka, Vladivostok, 2000, 37–38.
[5] M. Cwikel, “The K-divisibility constant for couples of Banach lattices”, J. Approx. Theory, 124:1 (2003), 124–136.
[6] I. Berg, I. Lefstrem, Interpoliatsionnye prostranstva. Vvedenie, Mir, M., 1980.
[7] Iu.A. Brudnyi, S. G. Krein, E. M. Semenov, “Interpoliatsiia lineinykh operatorov”, Itogi nauki i tekhniki, 24, Ser. Matem. analiz., VINITI, M., 1986, 3–163.
[8] K. I. Oskolkov, “Approksimativnye svoistva summiruemykh funktsii na mnozhestvakh polnoi mery”, Matem. sb., 103(145):4(8) (1977), 563–589.
[9] S. Janson, “Minimal and maximal method of interpolation”, J. Func. Anal., 44 (1981), 50–73.
[10] M. Cwikel, I. Kozlov, “Interpolation of weighted $L_1$ spaces – a new proof of the Sedaev–Semenov theorem”, Illinois J. Math., 46 (2002), 405–419.

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