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Lie-Trotter means in JB-algebras

Authors :
Wang, Zhenhua
Publication Year :
2023

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.<br />Comment: 18 pages

Subjects

Subjects :
Mathematics - Functional Analysis
Mathematical Physics
Primary 46H70, 47A64, 17C90, 15A16, Secondary 17C65, 81R15, 81P45, 94C99

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2310.12857
Document Type :
Working Paper

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