Convexity estimates for the outer measure of bilinear operators

Let \mathcal{I} be a surjective closed operator ideal with associated outer measure \gamma_{{\mathcal{I}}} , and let \gamma_{{\mathfrak{I}}} be the extension of \gamma_{{\mathcal{I}}} to bilinear operators. We establish a convexity inequality for the measure \gamma_{{\mathfrak{I}}} of a bilinear operator interpolated by the real method. Our arguments do not require that \mathcal{I} be symmetric.