  We give a method to obtain, from Voiculescu's inequality, norm estimates for
sums of free variables with amalgamation in general fully symmetric spaces. We
use these estimates to interpolate the Burkholder inequalities for non
commutative martingales. The method is also applicable to other similar
settings. In that spirit, we improve known results on the non commutative
Johnson-Schechtman inequalities and recover Khintchine inequalities associated
to free groups.
