Infinite pointwise lineability: general criteria and applications

In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set of infinite differentiable and integrable functions, for an...

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Detalles Bibliográficos
Autores: Prado Bassas, José Antonio, Gerlach Mena, Pablo José, Calderón Moreno, María del Carmen
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/152429
Acceso en línea:https://hdl.handle.net/11441/152429
https://doi.org/10.1007/s13398-023-01525-4
Access Level:acceso abierto
Palabra clave:Lineability
Spaceability
Pointwise lineability
Differentiable
Unbounded
Integrable
Descripción
Sumario:In this paper we introduce the concept of infinite pointwise dense lineability (spaceability), and provide a criterion to obtain density from mere lineability. As an application, we study the linear and topological structures within the set of infinite differentiable and integrable functions, for any order $p\ge1$, on $\mathbb{R}^N$ which are unbounded in a pre-fixed set.