BANACH LATTICE AM-ALGEBRAS
An analogue of Kakutani’s representation theorem for Banach lattice algebras is provided. We characterize Banach lattice algebras that embed as a closed sublattice-algebra of C(K) precisely as those with a positive approximate identity (eγ) such that x∗(eγ) → ⃦x∗⃦ for every positive functional x∗. W...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/420831 |
| Acceso en línea: | http://hdl.handle.net/10261/420831 https://www.scopus.com/inward/record.uri?eid=2-s2.0-105006528300&doi=10.1090%2Fproc%2F17173&partnerID=40&md5=d00c076d1ad0bee679945ba21887a78b |
| Access Level: | acceso abierto |
| Palabra clave: | AM-space Banach lattice algebra spaces of continuous functions |
| Sumario: | An analogue of Kakutani’s representation theorem for Banach lattice algebras is provided. We characterize Banach lattice algebras that embed as a closed sublattice-algebra of C(K) precisely as those with a positive approximate identity (eγ) such that x∗(eγ) → ⃦x∗⃦ for every positive functional x∗. We also show that every Banach lattice algebra with identity other than C(K) admits different product operations which are compatible with the order and the algebraic identity. This complements the classical result, due to Martignon, that on C(K) spaces pointwise multiplication is the unique compatible product. © 2025 American Mathematical Society. |
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