On some class of interpolation functors
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 2, pp. 7-20
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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.
Keywords: interpolation functor, Gustavsson — Peetre functor, Calderón — Lozanovskii method, Rademacher functions, Banach lattice, Khintchine inequality, Orlicz space.
@article{VSGU_2019_25_2_a0,
author = {S. V. Astashkin},
title = {On some class of interpolation functors},
journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
pages = {7--20},
publisher = {mathdoc},
volume = {25},
number = {2},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VSGU_2019_25_2_a0/}
}
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/