On monotone linear operators and the spectral radius of their representing matrices
On monotone linear operators and the spectral radius of their representing matrices
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关于单调线性算子及其表示矩阵的谱半径
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
H. H. Tigelaar
中科院分区：
文献类型：
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作者：
H. H. Tigelaar
本文研究了p空间上的线性算子 imes p $矩阵被认为是。这样的线性算子可以表示为$p^2 imes p^2 $矩阵。特别地，克罗内克积的和作为表示矩阵出现。设线性算子$mathcal {L}_S $和$mathcal {L}_U $分别由矩阵S和U表示，其中U的形式为$U = sum {A_k}多次 ar A_k $.本文证明了，若对所有半正定X，$mathcal {L}_U（X）等于mathcal {L}_S（X），U和S的谱半径必须满足不等式$
何列克
ho（S）$.
In this paper, linear operators on the space of $p imes p$ matrices are considered. Such linear operators can be represented by $p^2 imes p^2 $ matrices. In particular, sums of Kronecker products occur as representing matrices. Let the linear operators $mathcal{L}_S $ and $mathcal{L}_U $ be represented by the matrices S and U, where U is of the form $U = sum {A_k } otimes ar A_k $. It is shown that, in order that $mathcal{L}_U ( X )leqq mathcal{L}_S ( X )$ for all positive-semidefinite X, it is necessary that the spectral radii of U and S satisfy the inequality $
ho ( U )leqq
ho ( S )$.