Journal of Operator Theory

Volume 80, Issue 1, Summer 2018 pp. 125-152.

Maximal amenability of the generator subalgebra in $q$-Gaussian von Neumann algebras

Authors: Sandeepan Parekh (1), Koichi Shimada (2), and Chenxu Wen (3)
Author institution: (1) Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, U.S.A.
(2) Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
(3) Department of Mathematics, University of California, Riverside, CA 92521, U.S.A.

Summary: In this article, we develop a structural theorem for the $q$-Gaussian algebras, namely, we construct a Riesz basis for the $q$-Fock space in the spirit of R{\u a}dulescu. As an application, we show that the generator subalgebra is maximal amenable inside the $q$-Gaussian von Neumann algebra for any real number $q$ with $|q|$ less than $1/9$.

DOI: http://dx.doi.org/10.7900/jot.2017jun28.2167
Keywords: $q$-Gaussian, von Neumann algebra, Riesz basis, maximal amenability

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