| 算子空间的原子性 |
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| 引用本文： | 董浙,陶继成. 算子空间的原子性[J]. 数学年刊A辑(中文版), 2009, 30(3): 339-344 |
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| 作者姓名： | 董浙 陶继成 |
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| 作者单位： | 1. 浙江大学数学系,杭州,310027;2. 中国计量学院数学系,杭州,310018 |
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| 基金项目： | 国家自然科学基金，浙江省自然科学基金(No.Y606144)资助的项目 |
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| 摘 要： | 研究了算子空间的原子性.证明了算子空间V是原子当且仅当V是正合且有限内射; V内的任意一个有限维算子子空间是原子当且仅当V是原子且V内任意有限维算子子空间足V的完全补.因此作为推论,得到了无限维箅子空间V的任意有限维子空间是原子,则V是1-Hilbertian和1-齐次.
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| 关 键 词： | 算子空间 原子 内射 |
Nuclearity of Operator Spaces |
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| DONG Zhe and TAO Jicheng. Nuclearity of Operator Spaces[J]. Chinese Annals of Mathematics, 2009, 30(3): 339-344 |
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| Authors: | DONG Zhe and TAO Jicheng |
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| Affiliation: | Department of Mathematics, Zhejiang University, Hangzhou 310027, China.;Department of Mathematics, China Jiliang University, Hangzhou 310018,China. |
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| Abstract: | This paper studies the nuclearity for operator spaces. The authors show that anoperator space V is nuclear if and only if V is exact and finitely injective, and also provethat every finite dimensional operator subspace in V is nuclear if and only if V is nuclearand every finite dimensional operator subspace in V is completely complement in V . As acorollary, it is obtained that if every finite dimensional subspace of an infinite dimensionaloperator space V is nuclear, then V is 1-Hilbertian and 1-homogeneous. |
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| Keywords: | Operator space Nuclear Injective |
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