AN APPLICATION OF FREE TRANSPORT TO MIXED q-GAUSSIAN ALGEBRAS

作者：Nelson Brent^*; Zeng Qiang

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144(10): 4357-4366.

DOI：10.1090/proc/13068

We consider the mixed q-Gaussian algebras introduced by Speicher which are generated by the variables X-i = l(i) + l(i)*, i = 1, . . . , N, where l(i)*l(j)-q(ij)l(j)l(i)* = delta(i,j) and -1 < q(ij) = q(ji) < 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(F-N), provided that max(i,j) vertical bar q(ij)vertical bar is small enough. The proof relies on some estimates which are generalizations of Dabrowski's results for the special case q(ij) equivalent to q.

• 出版日期2016-10
• 单位西北大学