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arXiv · 1204.2044

Linear operators with wild dynamics

Jean-Matthieu Augé
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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.

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Jean-Matthieu Augé. 2012-04-10. Linear operators with wild dynamics. https://arxiv.org/abs/1204.2044

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