arXiv 0804.29062008-04math.OA

A Note about proving non-$Γ$ under a finite non-microstates free Fisher information Assumption

Yoann Dabrowski

备注：: 12 pages; New results with similar techniques; cf. abstracts for details
发表信息：: Journal of Functional Analysis Volume 258, Issue 11, June 2010, Pages 3662-3674
DOI：: 10.1016/j.jfa.2010.02.010

英文摘要：

We prove that if $X_{1},...,X_{n} (n >1)$ are selfadjoints 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 $Γ$ (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.

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