Convexity estimates for the outer measure of bilinear operators

Abstract

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.