Extensions of some matrix inequalities related to trace and partial traces

Abstract

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.

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)

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• Subadditivity of q-entropies for q>1
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Cited by in corpus (1)

• Improvements on some partial trace inequalities for positive semidefinite block matrices