On hypercyclicity and linear chaos in a nonclassical sequence space and beyond
Abstract
We analyze the hypercyclicity, chaoticity, and spectral structure of (bounded and unbounded) weighted backward shifts in a nonclassical sequence space, which the space of summable sequences is both isometrically isomorphic to and continuously and densely embedded into. Based on the weighted backward shifts, we further construct new bounded and unbounded linear hypercyclic and chaotic operators both in the nonclassical sequence space and the classical space , including those that are hypercyclic but not chaotic.
Cite
@article{arxiv.2209.04515,
title = {On hypercyclicity and linear chaos in a nonclassical sequence space and beyond},
author = {Marat V. Markin and Eric Montoya},
journal= {arXiv preprint arXiv:2209.04515},
year = {2022}
}
Comments
Refined estimates in Proposition 3.2 and Lemma 4.1, corresponding changes wherever pertinent, minor edits and readability improvements. There is a text overlap with arXiv:2106.09682, arXiv:2106.14872, and arXiv:2203.02032 in the Preliminaries section containing introductory information, definitions, and general remarks