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arXiv · 1911.07513

Dynamics of shift operators on non-metrizable sequence spaces

José Bonet·Thomas Kalmes·Alfred Peris
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Abstract

We investigate dynamical properties such as topological transitivity, (sequential) hypercyclicity, and chaos for backward shift operators associated to a Schauder basis on LF-spaces. As an application, we characterize these dynamical properties for weighted generalized backward shifts on K\"othe coechelon sequence spaces $k_p((v^{(m)})_{m\in\mathbb{N}})$ in terms of the defining sequence of weights $(v^{(m)})_{m\in\mathbb{N}}$. We further discuss several examples and show that the annihilation operator from quantum mechanics is mixing, sequentially hypercyclic, chaotic, and topologically ergodic on $\mathscr{S}'(\mathbb{R})$.

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José Bonet, Thomas Kalmes, Alfred Peris. 2019-11-18. Dynamics of shift operators on non-metrizable sequence spaces. https://doi.org/10.4171/rmi%2F1267

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