Symmetric finite representability of ℓ^p-spaces in rearrangement invariant spaces on [0,1]

2022/04/29 by Astashkin, Sergey V., Curbera, Guillermo P.
#46B07 #46B42 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46E30 #Secondary 46B70

paper · doi:10.48550/arxiv.2204.13904

Abstract

For a separable rearrangement invariant space X on [0,1] of fundamental type we identify the set of all p∈ [1,∞] such that ℓ^p is finitely represented in X in such a way that the unit basis vectors of ℓ^p (c₀ if p=∞) correspond to pairwise disjoint and equimeasurable functions. This can be treated as a follow up of a paper by the first-named author related to separable rearrangement invariant spaces on (0,∞).

Related

• Symmetric finite representability of ℓ^p-spaces in rearrangement invariant spaces on (0,∞)
• A characterization of ℓ^p-spaces symmetrically finitely represented in symmetric sequence spaces
• A rearrangement invariant space isometric to L_p coincides with L_p
• Subrearrangement-invariant function spaces
• Tchebyshev's characteristic of rearrangement invariant space