Y-数值半径的乘法因子

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.

Multiplicativity Factor of Y-Numerical Radius

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{|∑ni=1ξixiAxi|∶xixi=1,xi∈Cn}. where Cn 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 ∑ni=1ξi≠0 and ξj are not all equal. Next, multiplicativity factor of Y-numerical radius are characterized.