Geodesic
Further properties of accretive matrices
Shigeru Furuichi1 ; Hamid Reza Moradi2 ; Mohammad Sababheh3
1 Nihon University, College of Humanities and Sciences, Department of Information Science, and Saveetha School of Engineering, SIMATS, Department of Mathematics
2 Islamic Azad University, Mashhad Branch, Department of Mathematics
3 Princess Sumaya University for Technology, Department of Basic Sciences
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 387–404.

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To better understand the algebra $\mathcal{M}_n$ of all $n\times n$ complex matrices, we explore the class of accretive matrices. This class has received renowned attention in recent years due to its role in complementing those results known for positive definite matrices. Among many results, we present order-preserving results, Choi–Davis-type inequalities, mean-convex inequalities, sub-multiplicative results for the real part, and new bounds of the absolute value of accretive matrices. These results will be compared with the existing literature. In the end, we quickly pass through related entropy results for accretive matrices.
DOI : 10.54330/afm.146278
Keywords: Accretive matrix, operator monotone function, Choi–Davis inequality, mean of accretive matrices, operator matrix related to accretive matrices, entropy

Shigeru Furuichi 1 ; Hamid Reza Moradi 2 ; Mohammad Sababheh 3

1 Nihon University, College of Humanities and Sciences, Department of Information Science, and Saveetha School of Engineering, SIMATS, Department of Mathematics
2 Islamic Azad University, Mashhad Branch, Department of Mathematics
3 Princess Sumaya University for Technology, Department of Basic Sciences 
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Shigeru Furuichi; Hamid Reza Moradi; Mohammad Sababheh. Further properties of accretive matrices. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 387–404. doi : 10.54330/afm.146278. http://geodesic.mathdoc.fr/articles/10.54330/afm.146278/

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