Band projections and order idempotents in Banach lattice algebras
Year: 2024
Type: article
Abstract: 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.
Author: David Muñoz-Lahoz
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,100
Funder: Universidad Autónoma de Madrid
OpenAlex ID: W4404297415