arXiv subjects

Miran Jeong

Publications and source records attributed to Miran Jeong.

3 recordsLinked to original sources

arXiv2024

New Weighted Spectral Geometric Mean and Quantum Divergence

A new class of weighted spectral geometric means has recently been introduced. In this paper, we present its inequalities in terms of the Löwner order, operator norm, and trace. Moreover, we establish a log-majorization relationship between the new spectral geometric mean, and the Rényi relative operator entropy. We also give the quantum divergence of the quantity, given by the difference of trace values between the arithmetic mean and new spectral geometric mean. Finally, we study the barycenter that minimizes the weighted sum of quantum divergences for given variables.

math.QA↗

arXiv2023

Weak log-majorization and inequalities of power means

As non-commutative versions of the quasi-arithmetic mean, we consider the Lim-Pálfia's power mean, Rényi right mean and Rényi power means. We prove that the Lim-Pálfia's power mean of order $t \in [-1,0)$ is weakly log-majorized by the log-Euclidean mean and fulfills the Ando-Hiai inequality. We establish the log-majorization relationship between the Rényi relative entropy and the product of square roots of given variables. Furthermore, we show the norm inequalities among power means and provide the boundedness of Rényi power mean in terms of the quasi-arithmetic mean.

math.QA↗

arXiv2022

Right mean for the $α-z$ Bures-Wasserstein quantum divergence

A new quantum divergence induced from the $α-z$ Renyi relative entropy, called the $α-z$ Bures-Wasserstein quantum divergence, has been recently introduced. We investigate in this paper properties of the right mean, which is a unique minimizer of the weighted sum of $α-z$ Bures-Wasserstein quantum divergences to each points. Many interesting operator inequalities of the right mean with the matrix power mean including the Cartan mean are presented. Moreover, we verify the trace inequality with the Wasserstein mean and provide bounds for the Hadamard product of two right means.

math-ph↗