A Nakano Carrier Theorem for Polynomials
Functional Analysis
2021-07-23 v1
Abstract
We use a localisation technique to study orthogonally additive polynomials on Banach lattices. We derive alternative characterisations for orthogonal additivity of polynomials and orthosymmetry of -linear mappings. We prove that an orthogonally additive polynomial which is order continuous at one point is order continuous at every point and we give an example to show that this result does not extend to regular polynomials in general. Finally, we prove a Nakano Carrier theorem for orthogonally additive polynomials, generalising a result of Kusraev.
Cite
@article{arxiv.2107.10337,
title = {A Nakano Carrier Theorem for Polynomials},
author = {Christopher Boyd and Raymond A. Ryan and Nina Snigireva},
journal= {arXiv preprint arXiv:2107.10337},
year = {2021}
}