| 董浙,陶继成.算子空间的原子性[J].数学年刊A辑,2009,30(3):339~344 |
| 算子空间的原子性 |
| Nuclearity of Operator Spaces |
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| DOI： |
| 中文关键词: 算子空间 原子 内射 |
| 英文关键词:Operator space, Nuclear, Injective |
| 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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| 中文摘要: |
| 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. |
| 英文摘要: |
| This paper studies the nuclearity for operator spaces. The authors show that an
operator space V is nuclear if and only if V is exact and finitely injective, and also prove
that every finite dimensional operator subspace in V is nuclear if and only if V is nuclear
and every finite dimensional operator subspace in V is completely complement in V . As a
corollary, it is obtained that if every finite dimensional subspace of an infinite dimensional
operator space V is nuclear, then V is 1-Hilbertian and 1-homogeneous. |
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