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子空间超循环性与公共的子空间超循环向量

赵显锋 舒永录 周云华

赵显锋, 舒永录, 周云华. 子空间超循环性与公共的子空间超循环向量[J]. 华东师范大学学报(自然科学版), 2012, (1): 106-112, 120.
引用本文: 赵显锋, 舒永录, 周云华. 子空间超循环性与公共的子空间超循环向量[J]. 华东师范大学学报(自然科学版), 2012, (1): 106-112, 120.
ZHAO Xian-feng, SHU Yong-lu, ZHOU Yun-hua. Subspace-supercyclicity and common subspace-supercyclic vectors[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 106-112, 120.
Citation: ZHAO Xian-feng, SHU Yong-lu, ZHOU Yun-hua. Subspace-supercyclicity and common subspace-supercyclic vectors[J]. Journal of East China Normal University (Natural Sciences), 2012, (1): 106-112, 120.

子空间超循环性与公共的子空间超循环向量

详细信息
  • 中图分类号: O117.2

Subspace-supercyclicity and common subspace-supercyclic vectors

  • 摘要: 若无限维可分的~Banach~空间上的线性有界算子~$T$~满足: 对某个非零子空间~$M$, 存在向量~$x$~使~$\mathbb{C}\cdot O(x, T)\bigcap M$~在~$M$~中稠密, 则称~$T$~是子空间超循环算子. 构造例子说明了子空间超循环性并非是无限维现象, 以及子空间超循环算子并不一定是超循环的; 同时, 还给出了一个子空间超循环准则和一族算子的公共的子空间亚超循环(子空间超循环) 向量是稠密~$G_\delta$~集的充要条件.
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出版历程
  • 收稿日期:  2011-04-01
  • 修回日期:  2011-07-01
  • 刊出日期:  2012-01-25

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