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}
}
Comments
18 pages