2015/07/17 by Brent Nelson, Qiang Zeng, Nelson, Brent +1
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1507.04824
Typos and imprecision (mainly in the Introduction) are corrected. Type III case is erased for further more detailed investigation
arxiv created 2015/11/04 · arxiv updated 2015/11/05
We consider the mixed q-Gaussian algebras introduced by Speicher which are generated by the variables Xi=li+li^*,i=1,…,N, where li^* lj-qijlj li^*=δi,j and -1<qij=qji<1. Using the free monotone transport theorem of Guionnet and Shlyakhtenko, we show that the mixed q-Gaussian von Neumann algebras are isomorphic to the free group von Neumann algebra L(\mathbbFN), provided that maxi,j|qij| is small enough. The proof relies on some estimates which are generalizations of Dabrowski's results for the special case qij≡ q.