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November 2016 Maximal Banach ideals of Lipschitz maps
M. G. Cabrera-Padilla, J. A. Chávez-Domínguez, A. Jiménez-Vargas, Moisés Villegas-Vallecillos
Ann. Funct. Anal. 7(4): 593-608 (November 2016). DOI: 10.1215/20088752-3661620

Abstract

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.

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M. G. Cabrera-Padilla. J. A. Chávez-Domínguez. A. Jiménez-Vargas. Moisés Villegas-Vallecillos. "Maximal Banach ideals of Lipschitz maps." Ann. Funct. Anal. 7 (4) 593 - 608, November 2016. https://doi.org/10.1215/20088752-3661620

Information

Received: 29 January 2016; Accepted: 16 April 2016; Published: November 2016
First available in Project Euclid: 23 September 2016

zbMATH: 1365.46016
MathSciNet: MR3550938
Digital Object Identifier: 10.1215/20088752-3661620

Subjects:
Primary: 46B28
Secondary: 26A16, ‎46E15, 47L20

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.7 • No. 4 • November 2016
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