| Banach空间中有限秩拟线性投影算子的逼近问题 |
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| 引用本文： | 李智华,秦克林,王玉文.Banach空间中有限秩拟线性投影算子的逼近问题[J].数学的实践与认识,2006,36(6):268-270. |
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| 作者姓名： | 李智华 秦克林 王玉文 |
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| 作者单位： | 哈尔滨师范大学数学系,哈尔滨,150080 |
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| 摘 要： | 证得:在Banach空间中,相对紧集上的恒等算子可由一列有限秩连续拟线性投影算子一致逼近.由此得到:线性算子为紧线性算子必须且仅须它可由一列有限秩连续齐性算子一致逼近.
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| 关 键 词： | Banach空间 拟线性投影 恒等算子 逼近 |
| 修稿时间： | 2004年12月27 |
Approximation of Finite Rank Quasilinear Projector in Banach Space |
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| LI Zhi-hua,QIN Ke-kin,WANG Yu-wen.Approximation of Finite Rank Quasilinear Projector in Banach Space[J].Mathematics in Practice and Theory,2006,36(6):268-270. |
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| Authors: | LI Zhi-hua QIN Ke-kin WANG Yu-wen |
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| Abstract: | It is proved that the identity mapping on every precompact set in Banach space can be approximated uniformly by a sequence of finite rank continuous quasilinear projectors.It follows that a linear operator is a compact linear operator iff it an be approximated uniformly by a sequence of finite rank continuous homogeneous operators. |
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| Keywords: | Banach space quasilinear projection identity approximation |
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