Extensions of some matrix inequalities related to trace and partial traces
Yongtao Li
备注：
20 pages. I would like to thank my advisor Prof. Yuejian Peng (Hunan University) for reading carefully through an earlier version of this paper. This work was supported by NSFC (Grant No. 11931002)
发表信息：
Linear Algebra and its Applications 639 (2022) 205-224
We first present a determinant inequality related to partial traces for positive semidefinite block matrices. Our result extends a result of Lin [Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear Algebra 66 (2018)]. Moreover, we provide a unified treatment of a result of Ando [ILAS Conference (2014)] and a recent result of Li, Liu and Huang [Operators and Matrices 15 (2021)]. Furthermore, we also extend some determinant inequalities involving partial traces to a larger class of matrices whose numerical ranges are contained in a sector. In addition, some extensions on trace inequalities for positive semidefinite $2\times 2$ block matrices are also included.
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