Lipschitz tensor product
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Cabrera Padilla, María De Gádor; Chávez Domínguez, Javier Alejandro; Jiménez Vargas, Antonio; Villegas Vallecillos, MoisésFecha
2015Resumen
Inspired by the ideas of R. Schatten in his celebrated monograph on a theory of cross-spaces, we introduce the notion of a Lipschitz tensor product X&E of a pointed metric space X and a Banach space E as a certain linear subspace of the algebraic dual of Lip0(X,E*). We prove that X&E is linearly isomorphic to the linear space of all finite-rank continuous linear operators from (X#, τp) into E, where X# denotes the space Lip0(X,K) and τp is the topology of pointwise convergence of X#. The concept of Lipschitz tensor product of elements of X# and E* yields the space X#&E* as a certain linear subspace of the algebraic dual of X&E. To ensure the good behavior of a norm on X&E with respect to the Lipschitz tensor product of Lipschitz functionals (mappings) and bounded linear functionals (operators), the concept of dualizable (respectively, uniform) Lipschitz cross-norm on X&E is defined. We show that the Lipschitz injective norm ε, the Lipschitz projective norm π and the Lipschitz p-nuclear...
Palabra/s clave
Lipschitz map
Tensor product
p-summing operator
Duality
Lipschitz compact operator