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].
Original language | English |
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Pages (from-to) | 737-744 |
Number of pages | 8 |
Journal | Proceedings of the American Mathematical Society |
Volume | 151 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2023 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- Akemann-Ostrand property
- q-Gaussian C-algebras