Publication
Banach Journal of Mathematical Analysis
Paper

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

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Abstract

Let 1 < p ≠ 2 < ∞, ε > 0 and let T be an isomorphism from ℓp(ℓ2) into Lp[0, 1]. Then there is a subspace Y ⊂ ℓp(ℓ2), (1+ ε)-isomorphic to ℓp(ℓ2) such that T|Y is an (1+ ε)-isomorphism and T (Y) is Kp-complemented in Lp [0, 1], with Kp depending only on p. Moreover, Kp ≤ (1 + ε)γp if p > 2 and Kp ≤ (1 + ε)γp/(p−1) if 1 < p < 2, where γr is the Lr norm of a standard Gaussian variable.

Date

01 Jan 2011

Publication

Banach Journal of Mathematical Analysis

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