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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 onX, then every operator fromX to an L1-space factors through a Hilbert space, or equivalently B('1;X ) = 2('1;X ). If in addition X has the Gaussian average property, then it is of type 2. This implies that the same conclusion holds ifX has the Gordon{Lewis property (in particularX could be a Banach lattice) or ifX is isomorphic to a subspace of a Banach lattice of nite cotype, thus solving the Maurey extension problem for these classes of spaces. The paper also contains a detailed study of the property of extending operators with values in 'p-spaces, 1 p <1.

The Maurey extension property for Banach spaces with the Gordon–Lewis property and related structures