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arXiv · 0804.2906

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

Yoann Dabrowski
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Abstract

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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Yoann Dabrowski. 2009-07-13. A Note about proving non-$Γ$ under a finite non-microstates free Fisher information Assumption. https://doi.org/10.1016/j.jfa.2010.02.010

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