Few Bilinear Operators on Spaces of Continuous Functions

2025/10/06 by Leandro Candido, Candido, Leandro
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2510.05322

openalex publication_date 2025/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by recent work exhibiting a locally compact scattered space L constructed under Ostaszewski's \clubsuit-principle, which yielded a complete classification of linear operators on C₀(L× L), we extend the analysis to the bilinear setting. We show that, for this space L, every bilinear operator G:C₀(L)× C₀(L)→ C₀(L) admits a unique decomposition into the sum of trivially predictable components. This establishes a bilinear analogue of the few operators phenomenon.

Citations

• A Banach space induced by an almost disjoint family, admitting only few\n operators and decompositions
• The unconditional basic sequence problem

Related

• Few operators on Banach spaces C₀(L× L)
• Compact bilinear operators on asymmetric normed spaces
• Local estimates and global continuities in Lebesgue spaces for bilinear operators
• Spaceability in sets of operators on C(K)
• Discrete bilinear operators and commutators