On the isomorphism class of q-Gaussian C*-algebras for infinite variables

Journal article (2023)

Authors

M.J. Borst Analysis - EEMCS
M.P.T. Caspers Analysis - EEMCS
M. Klisse Analysis - EEMCS
Mateusz Wasilewski Polish Academy of Sciences
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2023 M.J. Borst, M.P.T. Caspers, M. Klisse, Mateusz Wasilewski
DOI: https://doi.org/10.1090/proc/16165
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Published Date

2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

For a real Hilbert space HR and −1 < q < 1 Bozejko and Speicher introduced the C∗-algebra Aq(HR) and von Neumann algebra Mq(HR) of qGaussian variables. We prove that if dim(HR) = ∞ and −1 < q < 1, q ∕= 0 then Mq(HR) does not have the Akemann-Ostrand property with respect to Aq(HR). It follows that Aq(HR) is not isomorphic to A0(HR). This gives an answer to the C∗-algebraic part of Question 1.1 and Question 1.2 in raised by Nelson and Zeng [Int. Math. Res. Not. IMRN 17 (2018), pp. 5486–5535].

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