Isometries for the vector (p,q) norm and the induced (p,q) norm
Isometries for the vector (p,q) norm and the induced (p,q) norm
复制标题
DOI：
10.1080/03081089508818368
复制
发表时间：
1995-06
影响因子：
1.1
通讯作者：
Anne-Louise Klaus;Chi-Kwong Li
中科院分区：
文献类型：
--
作者：
Anne-Louise Klaus;Chi-Kwong Li
设M m，n是环上m×n矩阵的线性空间，其中1≤p≤∞，设是列向量x的-范数.设1≤p，q≤∞。定义M m，n上的向量（p，q）范数，其中Aj是A的第j列，j = 1，... n，并定义M m，n上的导出（p，q）范数，这些定义包括最大行和范数。最大列和范数、算子范数等作为特例。本文刻画了Mm，n上向量（p，q）模和诱导（p，q）模的线性等距.证明依赖于涉及这些规范和Frobenius规范的某些不等式。这些不等式具有独立的意义。
Let M m,n be the linear space of m×n matrices over , where For 1≤p≤∞, let be the -norm of the column vector x. Suppose 1≤p,q≤∞. Define the vector (p,q) norm on M m,n by where Aj is the jth column of A for j = 1, …n, and define the induced(p,q) norm on Mm,n by These definitions include the maximum row sum norm. maximum column sum norm, and operator norm, etc as special cases. In this paper, we characterize the linear isometrics for the vector (p,q) norm and the induced (p,q) norm on M m,n . The proofs depend on certain inequalities involving these norms and the Frobenius norm. These inequalities are of independent interest.