arXiv:2310.12857 Abstract | arXiv Analytics

arXiv:2310.12857 [math.FA]Abstract References Reviews Resources

Lie-Trotter means in JB-algebras

Published 2023-10-19Version 1

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 the two-variable Lie-Trotter mean includes 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 the multivariable Lie-Trotter mean. In the end, using arithmetic-geometric-harmonic mean inequalities we provide a characterization of the multivariate Lie-Trotter mean.

Comments: 17 pages, first draft

Categories: math.FA, math-ph, math.MP

Subjects: 46H70, 47A64, 17C90, 15A16, 17C65, 81R15, 81P45, 94C99

Keywords: jb-algebras, lie-trotter formulas, arithmetic-geometric-harmonic mean inequalities, hansens induction mean, multivariate lie-trotter mean

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