Free monotone transport for infinite variables

2015/11/19 by Nelson, Brent, Zeng, Qiang
#FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1511.06291

Abstract

We extend the free monotone transport theorem of Guionnet and Shlyakhtenko to the case of infinite variables. As a first application, we provide a criterion for when mixed q-Gaussian algebras are isomorphic to L(\mathbbF_∞); namely, when the structure array Q of a mixed q-Gaussian algebra has uniformly small entries that decay sufficiently rapidly. Here a mixed q-Gaussian algebra with structure array Q=(q_ij)_i,j∈ℕ is the von Neumann algebra generated by X_n^Q=l_n+l_n^*, n∈ℕ and (l_n) are the Fock space representations of the commutation relation l_i^*l_j-q_ijl_jl_i^*=δ_i=j, i,j∈ℕ, -1

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