Band projections and order idempotents in Banach lattice algebras
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910657645903872 |
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| author | Muñoz-Lahoz, David |
| author_facet | Muñoz-Lahoz, David |
| contents | 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 $a \in A_+$ is a band projection if the multiplication operator $L_aR_a\in \mathcal L_r(A)$ 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 $0\leq a\leq e$ and $a^2=a$). 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09149 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Band projections and order idempotents in Banach lattice algebras Muñoz-Lahoz, David Functional Analysis 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 $a \in A_+$ is a band projection if the multiplication operator $L_aR_a\in \mathcal L_r(A)$ 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 $0\leq a\leq e$ and $a^2=a$). 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. |
| title | Band projections and order idempotents in Banach lattice algebras |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2407.09149 |