Hypercyclic operators with an infinite dimensional closed subspace of periodic points. (Q1432779)

Let \(X\) be an infinite-dimensional real or complex separable Banach space \(X\). If \(T\) is a bounded operator on \(X\), a vector \(x\) of \(X\) is said to be hypercyclic for \(T\) if the orbit of \(x\) under \(T\), that is, the set \(\{T^{n}x: n \geq 0 \}\), is dense in \(X\). If \(T\) has a hypercyclic vector, \(T\) is called a hypercyclic operator. In the paper under review, the author proves that if \(X\) is an infinite-dimensional separable Banach space, then there exists a hypercyclic operator on \(X\) which is equal to the identity operator on an infinite-dimensional closed subspace of \(X\).