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Singularity of the generator subalgebra in $ q$-Gaussian algebras


Author: Chenxu Wen
Journal: Proc. Amer. Math. Soc. 145 (2017), 3493-3500
MSC (2010): Primary 46L10
DOI: https://doi.org/10.1090/proc/13481
Published electronically: January 26, 2017
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Abstract: Given $ -1<q<1$ and a separable real Hilbert space $ \mathcal {H}_{\mathbb{R}}$ with dimension no less than 2, we prove that the generator subalgebra in the $ q$-Gaussian algebra $ \Gamma _q(\mathcal {H}_{\mathbb{R}})$ is singular.


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Additional Information

Chenxu Wen
Affiliation: Department of Mathematics, University of California, Riverside, California 92521
Email: chenxuw@ucr.edu

DOI: https://doi.org/10.1090/proc/13481
Received by editor(s): June 29, 2016
Received by editor(s) in revised form: September 12, 2016, and September 18, 2016
Published electronically: January 26, 2017
Communicated by: Adrian Ioana
Article copyright: © Copyright 2017 American Mathematical Society

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