Band projections and order idempotents in Banach lattice algebras
Motivated by recent work about band projections on spaces of regular operators over a Banach lattice, given a Banach lattice algebra A, we will say an element a ∈ A + is a band projection if the multiplication operator LaRa ∈Lr(A)is a band projection. Our aim in this note is to explore the relations...
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| Tipo de documento: | artigo |
| Data de publicação: | 2025 |
| País: | España |
| Recursos: | Universidad Autónoma de Madrid |
| Repositório: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.uam.es:10486/716555 |
| Acesso em linha: | http://hdl.handle.net/10486/716555 https://dx.doi.org/10.1016/j.jmaa.2024.129045 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Banach Lattice Algebra Band Projection Order Idempotent Regular Operator Matemáticas |
| Resumo: | Motivated by recent work about band projections on spaces of regular operators over a Banach lattice, given a Banach lattice algebra A, we will say an element a ∈ A + is a band projection if the multiplication operator LaRa ∈Lr(A)is a band projection. Our aim in this note is to explore the relations between this and the notion of order idempotent (those elements a in a Banach lattice algebra A with identity e such that 0 ≤ a ≤ e and a2 = a). We also revisit the properties of the ideal generated by the identity on a Banach lattice algebra, motivated by those of the centre of a Banach lattice |
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