Geodesic
On some class of interpolation functors
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 2, pp. 7-20 Cet article a éte moissonné depuis la source Math-Net.Ru

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As it is well known, the Gustavsson — Peetre construction, using the concept of unconditional convergence in Banach spaces, provides an important class of interpolation functors. In this paper, we define a new close construction, based on the use of the so-called random unconditional convergence. We find necessary and sufficient conditions, which being imposed on a generating function give us an interpolation functor defined on the category of Banach couples. It is shown that calculating the latter functor for a couple of Orlicz spaces results in the “natural” interpolation theorem. Moreover, we obtain conditions that guarantee the coincidence of this functor with the corresponding Gustavsson — Peetre functor, as well as with the Calderón — Lozanovskii method.
Mots-clés : interpolation space
Keywords: interpolation functor, Gustavsson — Peetre functor, Calderón — Lozanovskii method, Rademacher functions, Banach lattice, Khintchine inequality, Orlicz space. 
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S. V. Astashkin. On some class of interpolation functors. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 2, pp. 7-20. http://geodesic.mathdoc.fr/item/VSGU_2019_25_2_a0/

[1] J. Gustavsson, J. Peetre, “Interpolation of Orlicz spaces”, Studia Math., 60:1 (1977), 33–59 (in English) | DOI | MR | Zbl

[2] F. Albiac, N. J. Kalton, Topics in Banach Space Theory, Graduate Texts in Mathematics, 233, Springer-Verlag, New York, 2006, 373 pp. (in English) http://bookfi.net/book/443122 | MR | Zbl

[3] L. V. Kantorovich, G. P. Akilov, Functional Analysis, Nauka, M., 1977, 742 pp. (in Russian)

[4] S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolation of Linear Operators, Nauka, M., 1978, 400 pp. (in Russian)

[5] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces, v. II, Function Spaces, Springer-Verlag, Berlin–Heidelberg–New York, 1979, 243 pp. (in English) http://bookre.org/reader?file=773581 | Zbl

[6] M. A. Krasnoselskii, Ya. B. Rutickii, Convex Functions and Orlicz Spaces, Gos. izd. fiz. mat. lit., 1958, 271 pp. (in Russian)

[7] L. Maligranda, Orlicz Spaces, Interpolation, Seminars in Mathematics, 5, University of Campinas, Campinas, 1989, 206 pp. (in English) | MR | Zbl

[8] J. Bergh, J. L{ö}fstr{ö}m, Interpolation Spaces. An Introduction, Mir, M., 1980, 264 pp. (in Russian)

[9] Yu. A. Brudnyĭ, N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces, North-Holland, Amsterdam, 1991, 735 pp. (in English) http://bookre.org/reader?file=581684 | MR | Zbl

[10] C. Bennett, R. Sharpley, Interpolation of operators, Academic Press, Inc., Boston, 1988, 483 pp. (in English) http://bookre.org/reader?file=459025 | Zbl

[11] V. I. Ovchinnikov, “The Method of Orbits in Interpolation Theory”, Math. Reports, 1:2 (1984), 349–516 (in English) http://bookre.org/reader?file=580304 | MR

[12] S. V. Astashkin, Rademacher system in function spaces, Fizmatlit, M., 2017, 549 pp. (in Russian)

[13] S. J. Szarek, “On the best constant in the Khintchine inequality”, Studia Math., 58 (1976), 197–208 (in English) | DOI | MR | Zbl

[14] Triebel H., Interpolation theory, Function Spaces, Differential Operators, Mir, M., 1980, 664 pp. (in Russian)