Few Bilinear Operators on Spaces of Continuous Functions

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 $C_0(L\times L)$, we extend the analysis to the bilinear setting. We show that, for this space $L$, every bilinear operator $G:C_0(L)\times C_0(L)\to C_0(L)$ admits a unique decomposition into the sum of trivially predictable components. This establishes a bilinear analogue of the few operators phenomenon.