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A short note on strong convergence of $q$ -Gaussians

Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, 606-8502, Japan

E-mail Address: miyagawa.akihiro.43v@st.kyoto-u.ac.jp

https://doi.org/10.1142/S0129167X23500878Cited by:0 (Source: Crossref)

Abstract

In this paper, we prove strong convergence of $q$ -Gaussians with respect to a parameter $q$ , which implies the spectrum of any self-adjoint non-commutative polynomial in $q$ -Gaussians is continuously deformed with respect to $q$ . With Bożejko’s Haagerup-type inequality, we follow Brannan’s approach to proving the asymptotic strong convergence of the free orthogonal quantum group.

Communicated by Yasuyuki Kawahigashi

Keywords:

AMSC: 46L53, 46L54, 46L65

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