Construction of dense maximal-dimensional hypercyclic subspaces for Rolewicz operators

L. Bernal-González, M.C. Calderón-Moreno, J. Fernández-Sánchez, G.A. Muñoz-Fernández and J.B. Seoane-Sepúlveda
Authors registered in the RePEc Author Service: Guzmán Antonio Muñoz Fernández ()

Chaos, Solitons & Fractals, 2022, vol. 162, issue C

Abstract: In this paper, weighted backward shift operators Tw associated to a Schauder basis of a Banach space are considered. These operators are emblematic in the setting of linear chaos in topological vector spaces. In a constructive way, it is shown the existence of a dense linear subspace having maximal dimension, all of whose nonzero members are simultaneously Tw-hypercyclic for every w belonging to a sequence of admissible weights. Our proof does not use any general result about algebraic or topological genericity.

Keywords: Rolewicz operator; Weighted backward shift; Linear chaos; Hypercyclicity; Dense lineability (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:162:y:2022:i:c:s096007792200618x

DOI: 10.1016/j.chaos.2022.112408

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