This is an announcement for the paper "Linear operators with wild dynamics" by Jean-Matthieu Auge.

Abstract: If $X$ is a separable infinite dimensional Banach space, we construct a bounded and linear operator $R$ on $X$ such that $$ A_R={x \in X, |R^tx| \rightarrow \infty} $$ 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 H'ajek and Smith.

Archive classification: math.FA

Mathematics Subject Classification: Primary 47A05, Secondary 47A15, 47A16

Remarks: 14 pages

Submitted from: jean-matthieu.auge@math.u-bordeaux1.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1204.2044

or

http://arXiv.org/abs/1204.2044