Generalizations of Ky Fan's dominance theorem
Generalizations of Ky Fan's dominance theorem
复制标题
DOI：
10.1137/s0895479896311232
复制
发表时间：
1998-01-01
影响因子：
1.5
通讯作者：
Mathias, R
中科院分区：
文献类型：
--
作者：
Li, CK;Mathias, R
对于xεR-n且1小于或等于k小于或等于n，定义平行于x的k=(K)Sigma(i=1)\x([i])，其中x([1])，…，x([n])是x的项，使得x([1])大于或等于...大于或等于x([n])\.证明了对于R-n上的所有置换不变绝对范数，平行于x平行于(2)小于或等于平行于y平行于z平行于z当且仅当平行于x平行于(K)(2)小于或等于平行于y平行于k平行于z，k=1，2，…，n，这推广了Ky Fan的支配定理，并暗示了在Bhatia，Kittaneh和Li[线性和多线性代数，出现]最近关于交换子的不等式的一些工作中应用的矩阵空间上的酉不变范数的类似结果.得到了上述结果的进一步推广。
For x epsilon R-n and 1 less than or equal to k less than or equal to n, defineparallel to x parallel to k = (k) Sigma(i=1) \x([i])\,where x([1]),..., x([n]) are the entries of x such that \x([1])\ greater than or equal to...greater than or equal to \x([n])\. It is shown thatparallel to x parallel to(2) less than or equal to parallel to y parallel to parallel to z parallel tofor all permutation invariant absolute norms on R-n if and only ifparallel to x parallel to(k)(2) less than or equal to parallel to y parallel to k parallel to z parallel to k, k = 1,2,..., n.This generalizes Ky Fan's dominance theorem and implies similar results for unitarily invariant norms on the space of matrices that have application in some recent work of Bhatia, Kittaneh, and Li [Linear and Multilinear Algebra, to appear] on inequalities for commutators. Further generalizations of the above result are also obtained.