论文标题
Banach空间中的复发子空间
Recurrent subspaces in Banach spaces
论文作者
论文摘要
我们研究了操作员$ t：x \ longrightArrow x $ banach space $ x $的一组经过矢量的间距$ \ text {rec}（t）$。特别是：我们发现准刚性操作员具有复发子空间的足够条件；当$ x $是一个复杂的Banach空间时，我们表明具有复发子空间等效于以下事实：操作员的基本频谱与封闭的单元光盘相交。我们将先前的结果扩展到实际情况。结果，我们得到了：实际或可以分离的Banach空间上的弱混合操作员在且仅当它具有复发子空间时具有超环状子空间。结果暴露的结果表现出超环和复发间距理论之间的对称性，表明至少对于间隔性能，超循环和复发可以被视为平等。
We study the spaceability of the set of recurrent vectors $\text{Rec}(T)$ for an operator $T:X\longrightarrow X$ on a Banach space $X$. In particular: we find sufficient conditions for a quasi-rigid operator to have a recurrent subspace; when $X$ is a complex Banach space we show that having a recurrent subspace is equivalent to the fact that the essential spectrum of the operator intersects the closed unit disc; and we extend the previous result to the real case. As a consequence we obtain that: a weakly-mixing operator on a real or complex separable Banach space has a hypercyclic subspace if and only if it has a recurrent subspace. The results exposed exhibit a symmetry between the hypercyclic and recurrence spaceability theories showing that, at least for the spaceable property, hypercyclicity and recurrence can be treated as equals.
