Few bilinear operators on spaces of continuous functions

Abstract

Motivated by recent work exhibiting a locally compact scattered space L constructed under Ostaszewski’s ♣-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.