| 有界线性算子的不变测度 |
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| 引用本文： | 郭新伟. 有界线性算子的不变测度[J]. 山东大学学报(理学版), 1995, 0(2) |
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| 作者姓名： | 郭新伟 |
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| 作者单位： | 山东大学威海分校经济系 |
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| 摘 要： | 设Ｅ是一个复的可分的自反Ｂａｎａｃｈ空间，Ｔ是Ｅ上的有界可逆线性算子．若Ｅ是Ｃｏｔｙｐｅ－２空间，那么Ｔ的模为１的特征向量全体所张成的闭线性子空间等于关于Ｔ的不变的有强二阶矩的Ｂｏｒｅｌ概率测度的支集全体所张成的闭线性子空间．
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| 关 键 词： | 特征向量；不变测度；Cotype－2空间；Gauss测度；2－绝对可和算子；特征算子 |
INVARIANT MEASURES FOR BOUNDED LINEAR OPERATORS |
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| Guo Xinwei. INVARIANT MEASURES FOR BOUNDED LINEAR OPERATORS[J]. Journal of Shandong University, 1995, 0(2) |
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| Authors: | Guo Xinwei |
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| Abstract: | Let E is a complex separable reflexive Banach space,T is an invertible linear operator on E. If E is a Cotype-2 space,then the closed linear subspace spanned by eigenvetors having norm 1 for T concides with the subspace spanned by the supports of Borel probability measures on E which are invariant under T and have strong second moment. |
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| Keywords: | eigenvectors invariant measure Cotype-2 space Gaussian measure 2-absolutely summing operator eigenoperator |
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