Dynamics of a compact operator (Q541781)

In the paper under review, the author studies the dynamics of compact operators acting on Banach spaces. Precisely, he proves that, if \(T: X\to X\) is a compact linear (or, more generally, affine) operator from a Banach space into itself, then, for each \(x\in X\), the sequence of iterates \((T^nx)_{n=0}^\infty\) and its averages \((1/k)\sum_{k=0}^nT^{k-1}x\), \(n=0, 1,\ldots \), are either bounded or approach infinity.