We introduce the notion of acceptable noncommutative random variables and investigate their essential properties. More precisely, we provide several efficient estimation of tail probabilities of sums of noncommutative random variables under some mild conditions. Moreover, we investigate the complete convergence of a sequence of the form [Formula: see text] in which [Formula: see text] is a sequence of acceptable noncommutative random variables. Our results extend some classical inequalities as well.

中文翻译：

---

可接受的非交换随机变量的不等式

我们引入可接受的非交换随机变量的概念并研究它们的基本性质。更准确地说，我们提供了几种在一些温和条件下对非交换随机变量之和的尾概率的有效估计。此外，我们研究了 [公式：参见文本] 形式的序列的完全收敛，其中 [公式：参见文本] 是可接受的非交换随机变量序列。我们的结果也扩展了一些经典的不等式。