2025/03/12 by Eman Aldabbas, Mohammad Sababheh, Aldabbas, Eman +1 · 1 citation
Computer Science · Mathematics · #47A30 #47A63 #47A64 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2503.09875
openalex publication_date 2025/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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× n complex matrices such that \(A,B\) are sectorial with sector angle α for some \(α∈ [0,π/2)\), and if \(f:(0,∞)→(0,∞)\) is a certain operator monotone function such that \(\beginbmatrix cos2(α) f(A) & X X^* & cos2(α) f(B) \endbmatrix\) is APT, Then \(\beginbmatrix f(A)∇t f(B) & X X^* & f(A ∇tB ) \endbmatrix\) is APT for any \(0≤ t≤ 1\), where ∇t is the weighted arithmetic mean.