Sum of Free Variables in Fully Symmetric Spaces

Abstract

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.

arXiv comment17 pages

References in corpus (6)

• Noncommutative vector valued $L_p$-spaces and completely $p$-summing maps
• Embedding of OH and logarithmic `little Grothendieck inequality'
• Square functions for noncommutative differentially subordinate martingales
• Noncommutative Khintchine inequalities in interpolation spaces of $L_p$-spaces
• Noncommutative Davis type decompositions and applications
• Strong Haagerup inequality with operator coefficients