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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Detalles Bibliográficos
Autor: Muñoz Lahoz, David
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/716555
Acceso en línea:http://hdl.handle.net/10486/716555
https://dx.doi.org/10.1016/j.jmaa.2024.129045
Access Level:acceso abierto
Palabra clave:Banach Lattice Algebra
Band Projection
Order Idempotent
Regular Operator
Matemáticas
Descripción
Sumario: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