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- W2017221454 abstract "In this paper, linear operators on the space of $p times p$ matrices are considered. Such linear operators can be represented by $p^2 times 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 bar 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 $rho ( U )leqq rho ( S )$." @default.
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- W2017221454 date "1991-10-01" @default.
- W2017221454 modified "2023-09-26" @default.
- W2017221454 title "On Monotone Linear Operators and the Spectral Radius of Their Representing Matrices" @default.
- W2017221454 doi "https://doi.org/10.1137/0612056" @default.
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