Lie-Trotter means in JB-algebras

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.