子空间超循环性与公共的子空间超循环向量

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.

Subspace-supercyclicity and common subspace-supercyclic vectors

A bounded linear operator T on Banach space is subspace-supercyclic for a nonzero subspace M if there exists a vector whose projective orbit intersects the subspace M in a relatively dense set.We constructed examples to show that subspace-supercyclic is not a strictly infinite dimensional phenomenon,and that some subspace-supercyclic operators are not supercyclic.We provided a subspace-supercyclicity criterion and offered two necessary and sufficient conditions for a path of bounded linear operators to have a dense G_δset of common subspace-hypercyclic vectors and common subspace-supercyclic vectors.