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Paper Information

Journal:   BANACH JOURNAL OF MATHEMATICAL ANALYSIS   2017 , Volume 11 , Number 1; Page(s) 108 To 129.
 
Paper: 

DUALITY FOR IDEALS OF LIPSCHITZ MAPS

 
 
Author(s):  CABRERA PADILLA M.G., CHAVEZ DOMINGUEZ J.A., JIMENEZ VARGAS A.*, VILLEGAS VALLECILLOS MOISES
 
* 
 
Abstract: 

We develop a systematic approach to the study of ideals of Lipschitz maps from a metric space to a Banach space, inspired by classical theory on using Lipschitz tensor products to relate ideals of operator/tensor norms for Banach spaces. We study spaces of Lipschitz maps from a metric space to a dual Banach space that can be represented canonically as the dual of a Lipschitz tensor product endowed with a Lipschitz cross-norm, and we show that several known examples of ideals of Lipschitz maps (Lipschitz maps, Lipschitz pp-summing maps, maps admitting Lipschitz factorization through subsets of LpLp-space) admit such a representation. Generally, we characterize when the space of a Lipschitz map from a metric space to a dual Banach space is in canonical duality with a Lipschitz cross-norm. Finally, we introduce a concept of operators which are approximable with respect to one of these ideals of Lipschitz maps, and we identify them in terms of tensor-product notions.

 
Keyword(s): LIPSCHITZ MAP, TENSOR PRODUCT, PP-SUMMING OPERATOR, DUALITY IDEAL
 
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