Linear operators with wild dynamics

Augé, Jean-Matthieu

doi:10.1090/S0002-9939-2011-11082-7

Linear operators with wild dynamics
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by Jean-Matthieu Augé PDF

Proc. Amer. Math. Soc. 140 (2012), 2103-2116 Request permission

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 a 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.

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