| 保持Gauss测度的线性算子 |
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| 引用本文： | 郭新伟.保持Gauss测度的线性算子[J].江西师范大学学报(自然科学版),1998,22(4):322-325. |
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| 作者姓名： | 郭新伟 |
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| 作者单位： | 山东大学威海分校数学系 |
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| 摘 要： | 设Ｅ是一个复的可Ｂａｎａｃｈ空间，Ｔ是Ｅ上的线性有界算子，若存在Ｅ＾＊上的弱－＊稠密序列｛ｘ＾＊ｎ｝，使得在Ｔ＾＊下的轨道有界，那么存在关于Ｔ不变的非退化的Ｇａｕｓｓ测度的充分必要条件是Ｔ的模为１的特征向量全体张成Ｅ。
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| 关 键 词： | 不变测度 巴拿赫空间 高斯测度 线性算子 |
Gauss Measures Preserving Linear Operators |
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| Guo Xinwei.Gauss Measures Preserving Linear Operators[J].Journal of Jiangxi Normal University (Natural Sciences Edition),1998,22(4):322-325. |
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| Authors: | Guo Xinwei |
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| Abstract: | Let E be a complex separable Banach space,T a linear bounded operator.If there exists a weak- *dense sequence {x * n} in E which have bounded orbits under T *,then the necessary and sufficient conditions for T to accept a nondegenerate invariant Gauss measure is that E is spanned by the unimodular eigenvectors of T. |
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| Keywords: | Gauss measure invariant measure eigenvector |
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