The solution to the Maurey extension problem for Banach spaces with the Gordon Lewis property and related structures

1999/10/14 by Peter G. Casazza, Casazza, Peter G., N. J. Nielsen +2
Computer Science · Mathematics · #46B20 #46B42 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #math.FA #msc:46B20 #msc:46B42

paper · pdf · doi:10.48550/arxiv.math/9910073

26 pages, latex2e

arxiv created 1999/10/14 · openalex publication_date 1999/10/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result of this paper states that if a Banach space X has the property that every bounded operator from an arbitrary subspace of X into an arbitrary Banach space of cotype 2 extends to a bounded operator on X, then B(ℓ_∞,X^*)=Π₂(ℓ_∞,X^*). If in addition X has the Gaussian average property, then it is of type 2. This implies that the same conclusion holds if X has the Gordon-Lewis property (in particular X could be a Banach lattice) or if X is isomorphic to a subspace of a Banach lattice of finite cotype, thus solving the Maurey extension property for these classes of spaces. The paper also contains a detailed study of the property of extending operators with values in ℓ_p-spaces, 1≤ p

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