2024/07/10 by Jinmi Hwang, Hwang, Jinmi, Sejong Kim +1 · 1 citation
Computer Science · Physics and Astronomy · #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Quantum Mechanics and Non-Hermitian Physics #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2407.07438
openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
On the setting of positive definite operators we study the near-order properties of power means such as the quasi-arithmetic mean (Hölder mean) and Rényi power mean. We see the monotonicity of spectral geometric mean and Wasserstein mean on parameters with respect to the near-order and the near-order relationship between the spectral geometric mean and Wasserstein mean. Furthermore, the monotonicity of quasi-arithmetic mean on parameters and the convergence of Rényi power mean to the log-Euclidean mean with respect to the near-order have been established.