Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 4 (2016), 593-608.
Maximal Banach ideals of Lipschitz maps
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.
Ann. Funct. Anal. Volume 7, Number 4 (2016), 593-608.
Received: 29 January 2016
Accepted: 16 April 2016
First available in Project Euclid: 23 September 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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