Advanced Search

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 every operator from X to an L₁-space factors through a Hilbert space, or equivalently $B({\ell }_{\infty },X*)=\Pi ₂({\ell }_{\infty },X*)$. 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...