The solution to the Maurey extension problem for Banach spaces with the Gordon Lewis property and related structures
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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 $B(\ell_{\infty},X^*)=Π_2(\ell_{\infty},X^*)$. 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, $1\le p<\infty$.
26 pages, latex2e
26 pages, latex2e