Inequalities for Unitarily Invariant Norms
Inequalities for Unitarily Invariant Norms
复制标题
酉不变范数的不等式
DOI：
10.1137/s0895479898323823
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
Xingzhi Zhan
中科院分区：
文献类型：
--
作者：
Xingzhi Zhan
设A，B，X是复矩阵，其中A，B是正半定的。证明了
Let A,B,X be complex matrices with A,B positive semidefinite. It is proved that
(2+t)||ArXB2-r+A2-rXBr||\le 2||A2X+tAXB+XB2||
for any unitarily invariant norm $||\cdot||$ and real numbers r,t satisfying $1\le 2r\le 3,$ $-2 < t\le 2.$ The case r=1, t=0$ of this result is the well-known arithmetic-geometric mean inequality due to R. Bhatia and C. Davis [SIAM J. Matrix Anal. Appl., 14 (1993), pp. 132--136]. Several other unitarily invariant norm inequalities are derived.