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 Khinchin inequalities associated to free groups.

中文翻译：

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完全对称空间中自由变量的和

我们给出了一种从Voiculescu的不等式中获得一般完全对称空间中具有合并的自由变量之和的范数估计的方法。我们使用这些估计值来插值非交换mar的Burkholder不等式。该方法也适用于其他类似设置。本着这种精神，我们改善了非交换性Johnson-Schechtman不等式的已知结果，并恢复了与自由群体相关的Khinchin不等式。