There are known results showing a canonical association between Lipschitz cross-norms (norms on the Lipschitz tensor product of a metric space and a Banach space) and ideals of Lipschitz maps from a metric space to a dual Banach space. We extend this association, relating Lipschitz cross-norms to ideals of Lipschitz maps taking values in general Banach spaces. To do that, we prove a Lipschitz version of the representation theorem for maximal operator ideals. As a consequence, we obtain linear characterizations of some ideals of (nonlinear) Lipschitz maps between metric spaces.
"Maximal Banach ideals of Lipschitz maps." Ann. Funct. Anal. 7 (4) 593 - 608, November 2016. https://doi.org/10.1215/20088752-3661620