On $\alpha$-$z$-R\'{e}nyi divergence in the von Neumann algebra setting

Shinya Kato

On $\alpha$-$z$-R\'{e}nyi divergence in the von Neumann algebra setting

Operator Algebras 2023-11-06 v1 Mathematical Physics math.MP Quantum Physics

Authors: Shinya Kato

Abstract

We will investigate the $\alpha$ - $z$ -R\'{e}nyi divergence in the general von Neumann algebra setting based on Haagerup non-commutative $L^p$ -spaces. In particular, we establish almost all its expected properties when $0 < \alpha < 1$ and some of them when $\alpha > 1$ . In an appendix we also give an equality condition for generalized H\"{o}lder's inequality in Haagerup non-commutative $L^p$ -spaces.

Keywords

alpha-z-Rényi divergence von Neumann algebra Haagerup non-commutative L^p-spaces generalized Hölder inequality non-commutative measure theory

Cite

@article{arxiv.2311.01748,
  title  = {On $\alpha$-$z$-R\'{e}nyi divergence in the von Neumann algebra setting},
  author = {Shinya Kato},
  journal= {arXiv preprint arXiv:2311.01748},
  year   = {2023}
}

Comments

19 pages

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