Maximal Banach ideals of Lipschitz maps
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Cabrera Padilla, María de Gádor; Chávez Domínguez, Javier Alejandro; Jiménez Vargas, Antonio; Villegas Vallecillos, MoisésFecha
2016Resumen
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.
Palabra/s clave
Lipschitz map
Tensor product
p-summing operator
Duality
Ideal