Semi-Fredholm theory: hypercyclic and supercyclic subspaces (Q2766362)

The authors consider hereditarily hypercyclic operators \(T\) on Banach spaces \(B\), and give equivalent conditions for the existence of an infinite dimensional closed subspace \(B_1\) such that each \(z\in B_1\setminus \{0\}\) is an hypercyclic vector for \(T\). One condition, for example, is that the essential spectrum of \(T\) intersects the closed unit disk. Moreover, the authors give characterizations of the norm closure of the set of supercyclic operators with an infinite-dimensional closed subspace of supercyclic vectors.