Schatten q-norms and determinantal inequalities for matrices with numerical ranges in a sector

被引：4
|
作者：
Yang, Junjian [1 ,2 ]
Lu, Linzhang [1 ,3 ]
Chen, Zhen [1 ]
机构：
[1] Guizhou Normal Univ, Sch Math Sci, Guiyang, Guizhou, Peoples R China
[2] Hainan Normal Univ, Sch Math & Stat, Haikou, Hainan, Peoples R China
[3] Xiamen Univ, Sch Math Sci, Xiamen, Peoples R China
来源：
LINEAR & MULTILINEAR ALGEBRA | 2019年 / 67卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Schatten q-norms; determinantal inequality; numerical range; partial trace; EXTENSION; FIEDLER;
D O I：
10.1080/03081087.2017.1417351
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
When A is a density matrix in Mn. Mk, Audenaert [J Math Phys. 2007; 48] proved an interesting inequality for Schatten q- norms 1 + A q = tr1A q + tr2A q, where tr1 and tr2 stand for the first and second partial trace, respectively, a notion from quantum information theory. As an analogue of this result, Lin [Canad Math Bull. 2016; 59] recently presented the following determinantal inequality 1 + det A = det (tr1A) n + det (tr2A) k. In this note, we first correct a result of Kuai [Linear Multilinear Algebra. doi: 10.1080/ 03081087.2017.1304521] and then generalize the above two inequalities to a larger class of matrices whose numerical ranges are contained in a sector.
引用
收藏
页码：221 / 227
页数：7
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