Dynamics of shift operators on non-metrizable sequence spaces

Fuente: arXiv
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Main Authors: Bonet, José, Kalmes, Thomas, Peris, Alfred
Format: Preprint
Published: 2019
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author Bonet, José
Kalmes, Thomas
Peris, Alfred
author_facet Bonet, José
Kalmes, Thomas
Peris, Alfred
contents 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 Köthe 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 $\mathscr{S}'(\mathbb{R})$.
format Preprint
id arxiv_https___arxiv_org_abs_1911_07513
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle Dynamics of shift operators on non-metrizable sequence spaces
Bonet, José
Kalmes, Thomas
Peris, Alfred
Functional Analysis
47A16, 47B37
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 Köthe 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 $\mathscr{S}'(\mathbb{R})$.
title Dynamics of shift operators on non-metrizable sequence spaces
topic Functional Analysis
47A16, 47B37
url https://arxiv.org/abs/1911.07513