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

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

1999-10-14

arxiv.org/abs/math/9910073v1

Mathematics

Functional Analysis

26 pages, latex2e

Scientific paper

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 $B(\ell_{\infty},X^*)=\Pi_2(\ell_{\infty},X^*)$. 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 $\ell_p$-spaces, $1\le p<\infty$.

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