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Lie-Trotter means in JB-algebras

Functional Analysis 2023-11-14 v3 Mathematical Physics math.MP

Abstract

We initiate the study of Lie-Trotter means in JB-algebras, which is an extension of Lie-Trotter formulas in JB-algebras. We show that two-variable Lie-Trotter means include the weighted arithmetic mean, weighted harmonic mean, weighted geometric mean, and weighted spectral geometric mean. Consequently, several generalized Lie-Trotter formulas in JB-algebras are derived. Additionally, we demonstrate that the Sagae-Tanabe mean and Hansen's induction mean in JB-algebras are multivariable Lie-Trotter means. In the end, using arithmetic-geometric-harmonic mean inequalities we provide a characterization of multivariate Lie-Trotter means.

Keywords

Cite

@article{arxiv.2310.12857,
  title  = {Lie-Trotter means in JB-algebras},
  author = {Zhenhua Wang},
  journal= {arXiv preprint arXiv:2310.12857},
  year   = {2023}
}

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18 pages