On the Ando-Hiai property for spectral geometric means

2025/12/28 by Seo, Yuki, Wada, Shuhei, Yamazaki, Takeaki
#47A63 #47A64 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2512.22807

Abstract

In this paper, we consider a two-variable operator function that includes two weighted spectral geometric means, and show fundamental properties of the operator function. Moreover, it satisfies the Ando-Hiai type inequality under some restricted conditions. As an application, we show the log-majorization relations and norm inequalities for the spectral geometric means of positive definite matrices.

Citations

• Log-majorizations between quasi-geometric type means for matrices
• New Weighted Spectral Geometric Mean and Quantum Divergence
• Weak log-majorization between the geometric and Wasserstein means
• Inequalities and limits of weighted spectral geometric mean
• Functions preserving operator means
• Concavity of certain maps on positive definite matrices and applications to Hadamard products

Cited by

• Log-majorizations between quasi-geometric type means for matrices

Related

• Operator Spectral Geometric Versus Geometric Mean
• Inequalities and limits of weighted spectral geometric mean
• Operator inequalities and gyrolines of the weighted geometric means
• Ando-Hiai type inequalities for multivariate operator means
• Revisit on spectral geometric mean