Dynamics of a compact operator

Abstract

Let $T:X\to X$ be a compact linear (or more generally affine) operator from a Banach space into itself. For each $x\in X$, the sequence of iterates $T^{n}x,n=0,1,...$ and its averages $\frac{1}{k}{\sum }_{k=0}^n{T}^{k-1}x,n=0,1,...$ are either bounded or approach infinity.

24 pages