Some estimates for non-microstates free entropy dimension with applications to q-semicircular families
Some estimates for non-microstates free entropy dimension with applications to q-semicircular families
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非微观状态自由熵维数的一些估计及其在 q 半圆族中的应用
DOI：
10.1155/s1073792804140476
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发表时间：
2003
影响因子：
1
通讯作者：
D. Shlyakhtenko
中科院分区：
文献类型：
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作者：
D. Shlyakhtenko
给出了非微观态自由熵维数δ*（X1，…Xn）的一般估计.若X1，. Xn生成一个扩散冯诺依曼代数，则证明了δ* X1，. Xn ≥ 1.在这种情况下，X 1，.，X n是q-半圆形变量介绍了Bozejko和Speicher和q 2 n 1。我们还表明，对于|Q| <2−1，由有限族q-高斯随机变量生成的冯诺依曼代数满足小泽条件，因此是实心的：任何扩散子代数的相对交换子必须是超有限的。特别地，当这些代数是因子时，它们是素的并且不具有性质Γ。
We give a general estimate for the nonmicrostates free entropy dimension δ*(X 1 ,…X n ). If X 1 ,…X n generate a diffuse von Neumann algebra, we prove that δ*X 1 ,…X n ≥ 1. In the case that X 1 ,…,X n are q-semicircular variables as introduced by Bozejko and Speicher and q 2 n 1. We also show that for |q|<2−1, the von Neumann algebras generated by a finite family of q-Gaussian random variables satisfy a condition of Ozawa and are therefore solid: the relative commutant of any diffuse subalgebra must be hyperfinite. In particular, when these algebras are factors, they are prime and do not have property Γ.