We introduce the notion of a tree martingale in a noncommutative probability space and prove the Burkholder–Gundy inequalities for tree martingales in symmetric operator spaces. In particular, we establish some inequalities in this setting via an approach based on the concept of generalized singular valued functions of noncommutative random valuables.

中文翻译：

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非交换概率空间中的树Martin

我们引入了非交换概率空间中的树the概念，并证明了对称算子空间中树mar的Burkholder-Gundy不等式。特别是，我们通过基于非交换随机贵重物品的广义奇异值函数的概念的方法，在这种情况下建立了一些不等式。