2023/10/19 by Zhenhua Wang, Wang, Zhenhua
Mathematics · #15A16 #17C90 #47A64 #81P45 #81R15 #94C99 #Advanced Statistical Methods and Models #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematical Physics (math-ph) #Primary 46H70 #Secondary 17C65
paper · pdf · doi:10.48550/arxiv.2310.12857
openalex publication_date 2023/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.