f-algebra products on AL and AM-spaces

We characterize all f-algebra products on AM-spaces by constructing a canonical AMspace WX associated to each AM-space X, such that the f-algebra products on X correspond bijectively to the positive cone (WX )+. This generalizes the classical description of f-algebra products on C(K) spaces. We also...

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Detalles Bibliográficos
Autor: Muñoz Lahoz, David
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universidad Loyola Andalucía
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:dnet:biblosearchi::2a22c624ebe147df2f8b0babb85db1fd
Acceso en línea:https://hdl.handle.net/10486/768480
https://dx.doi.org/10.1007/s00209-026-04042-3
Access Level:acceso abierto
Palabra clave:f-algebra
AM-space
Banach lattice algebra
AL-space
Matemáticas
Descripción
Sumario:We characterize all f-algebra products on AM-spaces by constructing a canonical AMspace WX associated to each AM-space X, such that the f-algebra products on X correspond bijectively to the positive cone (WX )+. This generalizes the classical description of f-algebra products on C(K) spaces. We also identify the unique product (when it exists) that embeds X as a closed subalgebra of C(K), and study AM-spaces for which this product exists—the so-called AM-algebras. Finally, we investigate AM-spaces that admit only the zero product, providing a characterization in the AL-space case and examples showing that no simple characterization exists in general