Subspaces of L_p that embed into L_p(μ) with μ finite

2013/01/17 by Johnson, William B., Schechtman, Gideon
#46B03 #46B26 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1301.4086

Abstract

Enflo and Rosenthal proved that ℓ_p(ℵ₁), 1 < p < 2, does not (isomorphically) embed into L_p(μ) with μ a finite measure. We prove that if X is a subspace of an L_p space, 1< p < 2, and ℓ_p(ℵ₁) does not embed into X, then X embeds into L_p(μ) for some finite measure μ.

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