On notions of expansivity for operators on locally convex spaces
Abstract We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fréchet sequence spaces. Moreover, we give a partial answer to a problem proposed by Bernardes et al. (J Funct Anal 288(2):51, Paper No. 110696, 2025), by obtaining complete characterizations of the uniformly expansive weighted shifts on Köthe sequence spaces. Some general properties of the various concepts of expansivity in linear dynamics and several concrete examples are also presented.
Authors
- Félix Martı́nez-Giménez
- Nilson C. Bernardes (ORCID: https://orcid.org/0000-0003-1883-7629)
- Francisco Rodenas
Institutions
- Universidade Federal do Rio de Janeiro (BR)
- Instituto Nacional de Matemática Pura e Aplicada (BR)
- Universitat Politècnica de València (ES)
Publication Details
- Journal
- Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas
- Published
- 2026-03-05
- DOI
- https://doi.org/10.1007/s13398-026-01840-6
- Primary Topic
- Nonlinear Differential Equations Analysis
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- European Commission
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
- Generalitat Valenciana
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Agencia Estatal de Investigación