Integral representation of product factorable bilinear operators and summability of bilinear maps on [formula omitted]-spaces

Abstract

We present a constructive technique to represent classes of bilinear operators that allow a factorization through a bilinear product, providing a general version of the well-known characterization of integral bilinear forms as elements of the dual of an injective tensor product. We show that this general method fits with several known situations coming from different contexts—harmonic analysis, C⁎-algebras, C(K)-spaces, operator theory, polynomials—, providing a unified approach to the integral representation of a broad class of bilinear operators. Some examples and applications are also shown, regarding for example operator spaces and summability properties of bilinear maps.