Lattice isomorphic Banach lattices of polynomials

2025/09/15 by Boyd, Christopher, Miranda, Vinícius
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2509.12417

Abstract

We study Díaz-Dineen's problem for regular homogeneous vector-valued polynomials. In particular, we prove that whenever E^* and F^* are lattice isomorphic with at least one having order continuous norm, then P^r(ⁿ E; G^*) and P^r(ⁿ E; G^*) are lattice isomorphic for every n∈ \N and every Banach lattice G. We also study the analogous problem for the classes of regular compact, regular weakly compact, orthogonally additive and regular nuclear polynomials.

Citations

• Banach lattices of homogeneous polynomials not containing c₀
• Disjoint Dunford-Pettis-type properties in Banach lattices
• Holomorphic functions on complex Banach lattices
• Limits of vector lattices
• Bidual extensions of Riesz multimorphisms
• A Nakano Carrier Theorem for Polynomials
• Grothendieck-type subsets of Banach lattices
• The positive polynomial Schur property in Banach lattices
• Unbounded order convergence in dual spaces

Related

• Banach lattices of homogeneous polynomials not containing c₀
• Special non uniform lattice (snul) orthogonal polynomials on discrete dense sets of points.
• On the reflexivity of P_w(ⁿE;F)
• The polynomial property (V)
• On nonatomic Banach lattices and Hardy spaces