合并非交换概率空间塔上的R-变换理论
R-transform Theory On a Tower of Amalgamated Noncommutative Probability Spaces
摘要：
在[9]中，我们观察到合并R变换理论。与Voiculescu和Speicher的原始定义不同，我们用算子值形式级数定义了算子值随机变量的R变换.这样我们就可以建立合并R-变换演算。在本文中，我们将集中注意力于观察合并的非交换概率空间的塔上的R变换。我们将考虑R-变换演算和塔上的R-变换与关于塔的分布之间的关系。作为应用，我们将观察合并的非交换概率空间的给定塔和交换梯的相容性
英文摘要：
In [9], we observed Amalgamated R-transform Theory. Different from the original definition of Voiculescu and Speicher, we define R-transforms of operator-valued random variable(s) by operator-valued formal series. By doing that we can establish Amalgamated R-transform calculus. In this paper, we will concentrate on observing R-transforms on a tower of amalgamated noncommutative probability spaces. We will consider the R-transform calculus and relation between R-transforms on the tower and distributions with respect to the tower. As application, we will observe the compatibility of the given tower and commuting ladders of amalgamated noncommutative probability spaces
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