Accretive Partial Transpose Matrices and Their Connections to Matrix Means

Eman Aldabbas; Mohammad Sababheh

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arXiv · 2503.09875

Accretive Partial Transpose Matrices and Their Connections to Matrix Means

Eman Aldabbas·Mohammad Sababheh

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Abstract

Accretive partial transpose (APT) matrices have been recently defined, as a natural extension of positive partial transpose (PPT) matrices. In this paper, we discuss further properties of APT matrices in a way that extends some of those properties known for PPT matrices. Among many results, we show that if $A,B,X$ are $n\times n$ complex matrices such that $A,B$ are sectorial with sector angle $α$ for some $α\in [0,π/2)$, and if $f:(0,\infty)\to(0,\infty)$ is a certain operator monotone function such that $\begin{bmatrix} \cos^2(α) f(A) & X X^* & \cos^2(α) f(B) \end{bmatrix}$ is APT, Then $\begin{bmatrix} f(A)\nabla_t f(B) & X X^* & f(A \nabla_tB ) \end{bmatrix}$ is APT for any $0\leq t\leq 1$, where $\nabla_t$ is the weighted arithmetic mean.

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BibTeX RIS

Eman Aldabbas, Mohammad Sababheh. 2025-03-12. Accretive Partial Transpose Matrices and Their Connections to Matrix Means. https://arxiv.org/abs/2503.09875

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