论文标题
循环和超循环操作员之间的关系
Relationships between Cyclic and Hypercyclic Operators
论文作者
论文摘要
如果存在x $中的vector $ x \，则banach space $ x $上有界的线性运算符$ t $称为hypercyclic，这样$ orb {（x，x，t）} $在$ x $中是密集的。超环境标准是众所周知的足够条件，使操作员具有超环状。一个开放的问题是是否存在超循环标准也是必要条件的空间。出于多种原因，带有非常竞争的操作员的空间是一些自然候选人，这是对该问题的积极答案。在本文中，我们提供了一个定理，该定理为这些空间中的运营商建立了一些关系。
A bounded linear operator $T$ on a Banach space $X$ is called hypercyclic if there exists a vector $x \in X$ such that $orb{(x,T)}$ is dense in $X$. The Hypercyclicity Criterion is a well-known sufficient condition for an operator to be hypercyclic. One open problem is whether there exists a space where the Hypercyclicity Criterion is also a necessary condition. For a number of reasons, the spaces with very-few operators are some natural candidates to be a positive answer to that problem. In this paper, we provide a theorem that establishes some relationships for operators in these spaces.
