Stabilizing isomorphisms from ℓ_p(ℓ₂) into L_p[0,1]

2011/02/28 by Ran Levy, Levy, Ran, Gideon Schechtman +1
Mathematics · #46E30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46E30

paper · pdf · doi:10.48550/arxiv.1103.0047

arxiv created 2011/02/28 · arxiv updated 2011/03/02

Abstract

Let 1<p\not=2<∞, ε>0 and let T:ℓ_p(ℓ₂)\oversetinto→L_p[0,1] be an isomorphism. Then there is a subspace Y⊂ ℓ_p(ℓ₂) (1+ε)-isomorphic to ℓ_p(ℓ₂) such that: T_|Y is an (1+ε)-isomorphism and T(Y) is K_p-complemented in L_p[0,1], with K_p depending only on p. Moreover, K_p≤ (1+ε)γ_p if p>2 and K_p≤ (1+ε)γ_p/(p-1) if 1<p<2, where γ_r is the L_r norm of a standard Gaussian variable.

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