Linear operators with wild dynamics

Abstract

If $X$ is a separable infinite dimensional Banach space, we construct a bounded and linear operator $R$ on $X$ such that $$A_R=\{x\in X,\Vert R^{t}x\Vert \to \infty \}$$ is not dense and has non empty interior with the additional property that $R$ can be written $I+K$, where $I$ is the identity and $K$ is a compact operator. This answers two recent questions of Hájek and Smith.

arXiv comment14 pages