Y-数值半径的乘法因子

Multiplicativity Factor of Y-Numerical Radius

设A是一个n阶复数矩阵,y=(ξ1,…,ξn)是n维复数组,称ry(A)=max{|∑ξixi*Axi|∶xi*xi=1,xi∈Cn}为矩阵A的Y-数值半径,其中Cn表示复数域C上的n维向量空间.当y=(1,0,…,0)时,Y-数值半径变为标准数值半径r(A)=max{|x*Ax|∶x*x=1}.证得当sum from i=1 to n(ξi)≠0且ξi不都相等时,ry是广义矩阵范数,同时还讨论了ry的乘法因子.

Let A be an n × n complex matrix, and let y= （ξ1,…,ξn） be an n-dimensional complex vector. Then the Y- numerical radius of A, denoted by ry （A）, is defined as follows： ry（A）=max{｜∑ξixi^＊Axi｜∶xi^＊xi=1,xi∈C^n}. where C^n is an n-dimensional vector space over complex field. For y = （1,0,…,0） it reduces to the classical numerical radius r（A）. ry is a generalized matrix norm if and only if ∑i=1↑n（ξi）≠0 and ξi are not all equal. Next, muhiplicativity factor of Y-numerical radius are characterized.