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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| 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 |
| 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 |
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