A short note on strong convergence of q-Gaussians

2023/06/29 by Miyagawa, Akihiro
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2306.16679

Abstract

In this note, 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.

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