Grothendieck's theorem

Grothendieck's theorem is a fundamental result in functional analysis, specifically about how certain types of mathematical functions called bilinear forms behave when defined on product spaces of Banach spaces (complete, normed vector spaces). It states that every continuous bilinear form on a product of two such spaces can be approximated by simpler forms that factor through a specific sequence space, like \(\ell_2\). In essence, this theorem reveals that complex interactions between elements in these spaces can be understood and approximated by more structured, well-understood objects, simplifying the analysis and understanding of such functions.