Work

A Dense Lineability Criterion for Linear Dynamics

Year: 2026

Type: article

Abstract: We introduce and study Li-Yorke chaos for sequences of continuous linear operators from an $$F$$ F -space to a normed space. We show that in every infinite-dimensional separable complex Banach space, there exists a sequence of operators with a dense set of irregular vectors but without a dense irregular manifold. We introduce the $$\textrm{D}$$ D -phenomenon to establish a common dense lineability criterion that encompasses properties such as recurrence, universality, and Li-Yorke chaos.

Source: Integral Equations and Operator Theory

DOI: 10.1007/s00020-026-02852-y

Authors: Alexander Arbieto, Manuel Saavedra

Institution: Universidade Federal do Rio de Janeiro

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro