A note about proving non-Γ under a finite non-microstates free Fisher information assumption

被引：14

作者：

Dabrowski, Yoann ^{[1
,2
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[2] Univ Paris Est, Lab Informat, Inst Gaspard Monge, F-77454 Marne La Vallee 2, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 258卷 / 11期

关键词：

Property Gamma; Free Fisher information; Non-microstates free entropy; FREE PROBABILITY-THEORY; VON-NEUMANN-ALGEBRAS; FREE ENTROPY; SEMIGROUPS; ANALOGS;

D O I：

10.1016/j.jfa.2010.02.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if X(1),..., X(n) (n > 1) arc self-adjoints in a W*-probability space with finite non-microstates free Fisher information, then the von Neumann algebra W*(X(1),..., X(n)) they generate doesn't have property Gamma (especially is not amenable). This is an analog of a well-known result of Voiculescu for microstates free entropy. We also prove factoriality under finite non-microstates entropy. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：3662 / 3674

页数：13

共 19 条

[1] Large deviation bounds for matrix Brownian motion [J].