| 初等算子与Putnam-Fuglede定理 |
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| 引用本文： | 胡善文.初等算子与Putnam-Fuglede定理[J].数学杂志,2004,24(2):163-167. |
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| 作者姓名： | 胡善文 |
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| 作者单位： | 华东师范大学数学系,上海,200062 |
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| 基金项目： | ShanghaiPriorityAcademicDisciplineandNationalNaturalScienceFoundationofChina |
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| 摘 要： | 本文证明若A =(A1 ,A2 ,… )和B =(B1 ,B2 ,… )是Hilber空间H上的交换的正常算子列 ,满足条件 ∑∞j=1A j Aj=I和 ∑∞j=1B jBj =I.则对H上任何有界线性算子X ,由 ∑∞j=1AjXBj =X 可推得 :等式AjX =XBj和A jX =XB j 对所有的j成立
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| 关 键 词： | 初等算子 Putnam-Fuglede定理 |
THE ELEMENTARY OPERATOR AND PUTNAM-FUGLEDE THEOREM |
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| Abstract.THE ELEMENTARY OPERATOR AND PUTNAM-FUGLEDE THEOREM[J].Journal of Mathematics,2004,24(2):163-167. |
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| Authors: | Abstract |
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| Abstract: | We show that if A= (A1 ,A2…) and B= (B1,B2…) are two sequences of commutative normal operators on a Hibert space H satisfying the conditions ∞∑j-1A·j Aj = I and ∞∑B·j Bj = I respectively. Then for any operator X on H, ∞∑AjXBj = X implies AjX = XBj and A·jX=XB·j for all j=1,2…. |
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| Keywords: | elementary operator Putnam\|Fuglede theorem |
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