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

Operator Algebras 2023-06-30 v1 Functional Analysis

Abstract

In this note, we prove strong convergence of qq-Gaussians with respect to a parameter qq, which implies the spectrum of any self-adjoint non-commutative polynomial in qq-Gaussians is continuously deformed with respect to qq. With Bo\.{z}ejko's Haagerup-type inequality, we follow Brannan's approach to proving the asymptotic strong convergence of the free orthogonal quantum group.

Keywords

Cite

@article{arxiv.2306.16679,
  title  = {A short note on strong convergence of $q$-Gaussians},
  author = {Akihiro Miyagawa},
  journal= {arXiv preprint arXiv:2306.16679},
  year   = {2023}
}

Comments

6 pages. Comments are welcome