Lipschitz free p-spaces for 0<p<1 in the light of the Schur p-property and the compact reduction

The geometric analysis of non-locally convex quasi-Banach spaces presents rich and nuanced challenges. In this paper, we introduce the Schur p-property and the strong Schur p-property for 0<p¿1, providing new tools to deepen the understanding of these spaces, and the Lipschitz free p-spaces i...

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Detalles Bibliográficos
Autores: Albiac Alesanco, Fernando José, Ansorena, José L., Bíma, Jan, Cúth, Marek
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:dnet:academicae__::73d4c8564ce007df3a58bac99e0c17db
Acceso en línea:https://hdl.handle.net/2454/56684
Access Level:acceso abierto
Palabra clave:Compact reduction
Lispchitz free p-space
Schur p-property
Strong Schur p-property
Descripción
Sumario:The geometric analysis of non-locally convex quasi-Banach spaces presents rich and nuanced challenges. In this paper, we introduce the Schur p-property and the strong Schur p-property for 0<p¿1, providing new tools to deepen the understanding of these spaces, and the Lipschitz free p-spaces in particular. Moreover, by developing an adapted version of the compact reduction principle, we prove that Lipschitz free p-spaces over discrete metric spaces possess the approximation property, thereby answering positively a question raised by Albiac et al. in [4].