English

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

Operator Algebras 2010-09-28 v2

Abstract

We prove that if X1,...,Xn(n>1)X_{1},...,X_{n} (n >1) are selfadjoints in a WW^{*}-probability space with finite non-microstates free Fisher information, then the von Neumann algebra W(X1,...,Xn)W^{*}(X_{1},...,X_{n}) they generate doesn't have property Γ\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.

Keywords

Cite

@article{arxiv.0804.2906,
  title  = {A Note about proving non-$\Gamma$ under a finite non-microstates free Fisher information Assumption},
  author = {Yoann Dabrowski},
  journal= {arXiv preprint arXiv:0804.2906},
  year   = {2010}
}

Comments

12 pages; New results with similar techniques; cf. abstracts for details