自由斯坦因不规则性和尺寸

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Operator Theory Pub Date : 2019-02-06 DOI:10.7900/jot.2019aug29.2271

I. Charlesworth, Brent Nelson

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引用次数: 6

摘要

我们引入了一个自由的概率量，称为自由斯坦不规则，它是根据自由斯坦差异来定义的。结果是这个量通过一个简单的公式与非交换雅可比矩阵与Voiculescu的自由差商相关的共轭域的闭包的Murray-von Neumann维数有关。我们称这个维数为自由斯坦维数，并证明它是一个* -代数不变量。我们将这些量与自由费雪信息、非微观状态自由熵和非微观状态自由熵维度联系起来。在单变量情况下，我们证明了自由斯坦维与自由熵维是一致的，在多变量情况下，我们用一些例子来计算它。

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Free Stein irregularity and dimension

We introduce a free probabilistic quantity called free Stein irregularity, which is defined in terms of free Stein discrepancies. It turns out that this quantity is related via a simple formula to the Murray-von Neumann dimension of the closure of the domain of the adjoint of the non-commutative Jacobian associated to Voiculescu's free difference quotients. We call this dimension the free Stein dimension, and show that it is a ∗-algebra invariant. We relate these quantities to the free Fisher information, the non-microstates free entropy, and the non-microstates free entropy dimension. In the one-variable case, we show that the free Stein dimension agrees with the free entropy dimension, and in the multivariable case compute it in a number of examples.

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来源期刊

Journal of Operator Theory 数学-数学

CiteScore

1.30

自引率

12.50%

发文量

审稿时长

12 months

期刊介绍： The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.