A Note about proving non- under a finite non-microstates free Fisher information Assumption
Abstract
We prove that if X1,...,Xn (n >1) are selfadjoints in a W*-probability space with finite non-microstates free Fisher information, then the von Neumann algebra W*(X1,...,Xn) they generate doesn't have property (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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