子空间超循环性与公共的子空间超循环向量(英文)

Subspace-supercyclicity and common subspace-supercyclic vectors

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C·O(x,T)∩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Gδ集的充要条件.

A bounded linear operator T on Banach space is subspacesupercyclic 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 subspacesupercyclic is not a strictly infinite dimensional phenomenon, and that some subspacesupercyclic operators are not supercyclic. We provided a subspacesupercyclicity criterion and offered two necessary and sufficient conditions for a path of bounded linear operators to have a dense G set of common subspacehypercyclic vectors and common subspacesupercyclic vectors. Key words： subspacesupercyclicity; common subspacehypercyclic vectors; common subspacesupercyclic vectors