Hypercyclic and subspace-hypercyclic operators (Q2906963)

Let \(X\) be a complex separable infinite-dimensional Banach space. An operator \(T\in{\mathcal B}(X)\) is called hypercyclic if there exists a vector \(x\in X\) such that the set \(\{ T^{n}x: n=0,1,\ldots\}\) is dense in \(X\). If the intersection of this set and a \(T\)-invariant subspace \(M\subset X\) is dense in \(M\), the given operator is called \(M\)-hypercyclic. The authors give sufficient conditions for a hypercyclic operator \(T\) to be \(M\)-hypercyclic.