Open AccessSYMMETRIC FINITE REPRESENTABILITY OF ℓp IN ORLICZ SPACES
Author(s) -
С. В. Асташкин,
С. В. Асташкин
Publication year - 2021
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2020-26-4-15-24
Subject(s) - mathematics , banach space , linear subspace , subspace topology , separable space , space (punctuation) , characterization (materials science) , pure mathematics , dimension (graph theory) , set (abstract data type) , discrete mathematics , finitely generated abelian group , vector space , combinatorics , mathematical analysis , computer science , materials science , programming language , nanotechnology , operating system
It is well known that a Banach space need not contain any subspace isomorphic to a space ℓp (1 6 p ) or c0 (it was shown by Tsirelson in 1974). At the same time, by the famous Krivines theorem, every Banach space X always contains at least one of these spaces locally, i.e., there exist finite-dimensional subspaces of X of arbitrarily large dimension n which are isomorphic (uniformly) to ℓnp for some 1 6 p or cn0 . In thiscase one says that ℓp (resp. c0) is finitely representable in X. The main purpose of this paper is to give a characterization (with a complete proof) of the set of p such that ℓp is symmetrically finitely representable in a separable Orlicz space.