Cabrera-Padilla, M. G.; Chávez-Domínguez, J. A.; Jiménez-Vargas, A.; Villegas-Vallecillos, Moisés Maximal Banach ideals of Lipschitz maps. (English) Zbl 1365.46016 Ann. Funct. Anal. 7, No. 4, 593-608 (2016). Summary: 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. Cited in 10 Documents MSC: 46B28 Spaces of operators; tensor products; approximation properties 26A16 Lipschitz (Hölder) classes 46E15 Banach spaces of continuous, differentiable or analytic functions 47L20 Operator ideals Keywords:Lipschitz map; tensor product; \(p\)-summing operator; duality; ideal × Cite Format Result Cite Review PDF Full Text: DOI Euclid