论文标题
与跟踪和部分迹线有关的一些矩阵不等式的扩展
Extensions of some matrix inequalities related to trace and partial traces
论文作者
论文摘要
我们首先提出了与阳性半限制块矩阵的部分痕迹相关的决定因素不平等。我们的结果扩展了Lin [捷克的结果。数学。 J. 66（2016）]并改善了kuai的结果[线性多线性代数66（2018）]。此外，我们提供了对Ando [ILAS Conference（2014）]结果的统一处理，以及Li，Liu和Huang [运营商和矩阵15（2021）]的最新结果。此外，我们还将涉及部分迹线的一些决定因素扩展到较大的矩阵，其数值范围包含在一个扇区中。此外，还包括了痕量不平等的某些扩展，即$ 2 \ times $ 2 \ times 2 $块矩阵。
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.
