Annals of Functional Analysis

(p,σ)-Absolutely Lipschitz operators

D. Achour, P. Rueda, and R. Yahi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Due to recent advances in the theory of ideals of Lipschitz mappings, we introduce (p,σ)-absolutely Lipschitz mappings as an interpolating class between Lipschitz mappings and Lipschitz absolutely p-summing mappings. Among other results, we prove a factorization theorem that provides a reformulation to the one given by Farmer and Johnson for Lipschitz absolutely p-summing mappings.

Article information

Ann. Funct. Anal., Volume 8, Number 1 (2017), 38-50.

Received: 9 March 2016
Accepted: 7 June 2016
First available in Project Euclid: 31 October 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47L20: Operator ideals [See also 47B10]
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20] 26A16: Lipschitz (Hölder) classes

Lipschitz operators $(p,\sigma)$-absolutely Lipschitz mappings Pietsch factorization theorem


Achour, D.; Rueda, P.; Yahi, R. $(p,\sigma)$ -Absolutely Lipschitz operators. Ann. Funct. Anal. 8 (2017), no. 1, 38--50. doi:10.1215/20088752-3720614.

Export citation


  • [1] D. Achour, E. Dahia, P. Rueda, and E.A. Sánchez Pérez, Factorization of strongly $(p,\sigma)$-continuous multilinear operators, Linear Multilinear Algebra. 62 (2014), no. 12, 1649–1670.
  • [2] D. Achour, P. Rueda, E.A. Sánchez-Pérez, and R. Yahi, Lipschitz operator ideals and the approximation property, J. Math. Anal. Appl. 436 (2016), no. 1, 217–236.
  • [3] R. F. Arens and J. Eells Jr., On embedding uniform and topological spaces, Pacific J. Math. 6 (1956), 397–403.
  • [4] G. Botelho, D. Pellegrino, and P. Rueda, A unified Pietsch domination theorem, J. Math. Anal. Appl. 365 (2010), no. 1, 269–276.
  • [5] J. A. Chávez-Domínguez and J. Alejandro, Duality for Lipschitz $p$-summing operators, J. Funct. Anal. 261 (2011), 387–407.
  • [6] D. Chen and B. Zheng, Remarks on Lipschitz $p$-summing operators, Proc. Amer. Math. Soc. 139 (2011), no. 8, 2891–2898.
  • [7] D. Chen and B. Zheng, Lipschitz $p$-integral operators and Lipschitz $p$-nuclear operators, Nonlinear Analysis 75 (2012), 5270–5282.
  • [8] J. Diestel, H. Jarchow, and A. Tonge, Absolutely Summing Operators, Cambridge Stud. Adv. Math. 43, Cambridge Univ. Press, Cambridge, 1995. ISBN: 0-521-43168-9.
  • [9] J. D. Farmer and W. B. Johnson, Lipschitz $p$-summing operators, Proc. Amer. Math. Soc. 137 (2009), no. 9, 2989–2995.
  • [10] W. B. Johnson, B. Maurey, and G. Schechtman, Nonlinear factorization of linear operators, Bull. Lond. Math. Soc. 41 (2009), 663–668.
  • [11] A. Jiménez-Vargas, J. M. Sepulcre, and M. Villegas-Vallecillos, Lipschitz compact operators, J. Math. Anal. Appl. 415 (2014), no. 2, 889–901.
  • [12] J. A. López Molina and E. A. Sánchez-Pérez, On operator ideals related to $(p,\sigma)$-absolutely continuous operator, Studia Math. 131 (2000), no. 8, 25–40.
  • [13] U. Matter, Absolutely continuous operators and super-reflexivity, Math. Nachr. 130 (1987), 193–216.
  • [14] U. Matter, Factoring trough interpolation spaces and super-reflexive Banach spaces, Rev. Roumaine Math. Pures Appl. 34 (1989), 147–156.
  • [15] D. Pellegrino, P. Rueda, and E. A. Sánchez-Pérez, Improving integrability via absolute summability: a general version of Diestel’s Theorem, Positivity 20 (2016), no. 2, 369-383.
  • [16] D. Pellegrino and J. Santos, A general Pietsch domination theorem, J. Math. Anal. Appl. 375 (2011), no. 1, 371–374.
  • [17] E. A. Sánchez-Pérez, On the structure of tensor norms related to $(p,\sigma)$-absolutely continuous operators, Collect. Math. 47 (1996), no. 1, 35–46.
  • [18] N. Weaver, Lipschitz Algebras, World Scientific, Singapore, 1999.