Annals of Functional Analysis

Maximal Banach ideals of Lipschitz maps

M. G. Cabrera-Padilla, J. A. Chávez-Domínguez, A. Jiménez-Vargas, and Moisés Villegas-Vallecillos

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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.

Article information

Source
Ann. Funct. Anal. Volume 7, Number 4 (2016), 593-608.

Dates
Received: 29 January 2016
Accepted: 16 April 2016
First available in Project Euclid: 23 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.afa/1474652184

Digital Object Identifier
doi:10.1215/20088752-3661620

Mathematical Reviews number (MathSciNet)
MR3550938

Zentralblatt MATH identifier
06667756

Subjects
Primary: 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
Secondary: 26A16: Lipschitz (Hölder) classes 46E15: Banach spaces of continuous, differentiable or analytic functions 47L20: Operator ideals [See also 47B10]

Keywords
Lipschitz map tensor product $p$-summing operator duality ideal

Citation

Cabrera-Padilla, M. G.; Chávez-Domínguez, J. A.; Jiménez-Vargas, A.; Villegas-Vallecillos, Moisés. Maximal Banach ideals of Lipschitz maps. Ann. Funct. Anal. 7 (2016), no. 4, 593--608. doi:10.1215/20088752-3661620. https://projecteuclid.org/euclid.afa/1474652184


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References

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