Details

Autor(en) / Beteiligte

• Boyd, Christopher
• Ryan, Raymond
• Snigireva, Nina

Titel

A Nakano carrier theorem for polynomials

Ist Teil von

• Proceedings of the American Mathematical Society, 2023-04, Vol.151 (4), p.1621

Erscheinungsjahr

2023

Quelle

American Mathematical Society Journals

Beschreibungen/Notizen

• 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 m-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 [Orthosymmetric bilinear operators, Vladikavkaz, preprint, 2007].