A version of Calderón–Mityagin theorem for the class of rearrangement invariant groups. (November 2020)

• Record Type: Journal Article
• Authors: Astashkin, Sergey V.
• Is Part Of: Nonlinear analysis. Volume 200(2020)
• Publication Date: 2020-11
• Subjects: 46B70 -- 46B42; Quasi-normed group -- Rearrangement invariant group -- Orbit of an element -- Calderón–Mityagin theorem -- Interpolation group -- Peetre's K-functional -- K-monotone pair; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.112063
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let l 0 be the group (with respect to the coordinate-wise addition) of all sequences of real numbers x = ( x k ) k = 1 ∞ that are eventually zero, equipped with the quasi-norm ‖ x ‖ 0 = card { supp x } . A description of orbits of elements in the pair ( l 0, l 1 ) is given, which complements (in the sequence space setting) the classical Calderón–Mityagin theorem on a description of orbits of elements in the pair ( l 1, l ∞ ) . As a consequence, we obtain that the pair ( l 0, l 1 ) is K -monotone.