SPECTRAL PROPERTIES OF POSITIVELY HOMOGENEOUS OPERATORS INDUCED BY HIGHER ORDER TENSORS
SPECTRAL PROPERTIES OF POSITIVELY HOMOGENEOUS OPERATORS INDUCED BY HIGHER ORDER TENSORS
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高阶张量导出的正齐次算子的谱性质
DOI：
10.1137/130909135
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发表时间：
2013-01-01
影响因子：
1.5
通讯作者：
Qi, Liqun
中科院分区：
文献类型：
--
作者：
Song, Yisheng;Qi, Liqun
证明了高阶张量A的本征值(E-本征值、H-本征值、Z-本征值)的Fredholm型交替结果.对于由高阶张量A诱导的正齐次算子F-A和T-A，我们证明了Gelfand公式与谱半径之间的某种关系，并给出了它们的谱半径的上界.此外，对于非负张量A，我们得到了算子F-A和T-A的谱半径以及F-A和T-A的算子范数之间的实用关联性。
The Fredholm alternative type results are proved for eigenvalues (E-eigenvalues, H-eigenvalues, Z-eigenvalues) of a higher order tensor A. For the positively homogeneous operators F-A and T-A induced by a higher order tensor A, we show some relationship between the Gelfand formula and the spectral radius, and present the upper bound of their spectral radii. Furthermore, for a nonnegative tensor A, we obtain the practical relevance for the spectral radius of the operators F-A and T-A as well as the operator norms of F-A and T-A.