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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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

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

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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]

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


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.

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  • [1] M. G. Cabrera-Padilla, J. A. Chávez-Domínguez, A. Jiménez-Vargas, and Moisés Villegas-Vallecillos, Lipschitz tensor product, Khayyam J. Math. 1 (2015), no. 2, 185–218.
  • [2] M. G. Cabrera-Padilla, J. A. Chávez-Domínguez, A. Jiménez-Vargas, and Moisés Villegas-Vallecillos, Duality for ideals of Lipschitz maps, to appear in Banach J. Math. Anal., preprint arXiv:1506.05991 [math.FA].
  • [3] M. G. Cabrera-Padilla and A. Jiménez-Vargas, Lipschitz Grothendieck-integral operators, Banach J. Math. Anal. 9 (2015), no. 4, 34–57.
  • [4] J. A. Chávez-Domínguez, Duality for Lipschitz $p$-summing operators, J. Funct. Anal. 261 (2011), no. 2, 387–407.
  • [5] J. A. Chávez-Domínguez, Lipschitz $(q,p)$-mixing operators, Proc. Amer. Math. Soc. 140 (2012), no. 9, 3101–3115.
  • [6] J. A. Chávez-Domínguez, Lipschitz factorization through subsets of Hilbert space, J. Math. Anal. Appl. 418 (2014), no. 1, 344–356.
  • [7] D. Chen and B. Zheng, Lipschitz $p$-integral operators and Lipschitz $p$-nuclear operators, Nonlinear Anal. 75 (2012), no. 13, 5270–5282.
  • [8] A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Math. Stud. 176, North-Holland, Amsterdam, 1993.
  • [9] G. Godefroy and N. J. Kalton, Lipschitz-free Banach spaces, Studia Math. 159 (2003), no. 1, 121–141.
  • [10] A. Jiménez-Vargas, J. M. Sepulcre, and Moisés Villegas-Vallecillos, Lipschitz compact operators, J. Math. Anal. Appl. 415 (2014), no. 2, 889–901.
  • [11] N. J. Kalton, Spaces of Lipschitz and Hölder functions and their applications, Collect. Math. 55 (2004), no. 2, 171–217.
  • [12] H. P. Lotz, Grothendieck ideals of operators in Banach spaces, Lecture Notes, Univ. of Illinois, Urbana, IL, 1973.