Strongly Lipschitz (ℓp ,ℓq)-factorable mappings

• Achour, Dahmane ^[1] ; Tiaiba, Toufik ^[1]
  1. [1] Université de M'Sila

     Université de M'Sila

     Argelia

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 25, Nº. 1, 2024, págs. 237-251
• Idioma: inglés
• DOI: 10.4995/agt.2024.18928
• Enlaces
  • Texto completo
• Resumen

  • In this paper we study the space of strongly Lipschitz (ℓp ,ℓq) -factorable operators between metric spaces and a Banach spaces.In particular, a factorization of this class through ℓp and ℓq spaces is given.We show that this type of operators fits in the theory of composition α-Banach Lipschitz operator ideal.As a special case, we get a Lipschitz version of weakly p-nuclear operators.

• Referencias bibliográficas
  • D. Achour, P. Rueda, E. A. Sánchez-Pérez and R. Yahi, Lipschitz operator ideals and the approximation property, Journal of Mathematical Analysis...
  • D. Achour, E. Dahia and P. Turco, The Lipschitz injective hull of Lipschitz operator ideals and applications, Banach J. Math. Anal. (2020),...
  • D. Achour, E. Dahia and P. Turco, Lipschitz p-compact mappings, Monatshefte für Mathematik 198 (2019), 595-609. https://doi.org/10.1007/s00605-018-1252-1
  • D. Achour, P. Rueda and R. Yahi, (p,σ)-Absolutely Lipschitz operators, Annals of Functional Analysis 8, no. 1 (2017), 38-50. https://doi.org/10.1215/20088752-3720614
  • R. F. Arens and J. Eells Jr, On embedding uniform and topological spaces. Pacific J. Math. 6 (1956), 397-403. https://doi.org/10.2140/pjm.1956.6.397
  • A. Belacel and D. Chen, Lipschitz (p,r,s)-integral operators and Lipschitz (p,r,s)-nuclear operators, Journal of Mathematical Analysis and...
  • M. G. Cabrera-Padilla, J. A. Chávez-Domínguez, A. Jiménez-Vargas and M. Villegas-Vallecillos, Maximal Banach ideals of Lipschitz maps, Ann....
  • D. Chen and B. Zheng, Lipschitz p-integral operators and Lipschitz p-nuclear operators, Nonlinear Analysis 75, no. 13 (2012), 5270-5282. https://doi.org/10.1016/j.na.2012.04.044
  • J. Dazord, Applications semi-faibles, CR Acad. Sci. Paris. 278 (1974), 261-263.
  • J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Cambridge University Press (1995). https://doi.org/10.1017/CBO9780511526138
  • J. D. Fermer and W. B. Johnson, Lipschitz p-summing operators, Proc. Amer. Math. Soc. 137, no. 9 (2009), 2989-2995. https://doi.org/10.1090/S0002-9939-09-09865-7
  • A. Godard, Espaces Lipschitz-libres, propriété (M) et lissité asymptotique, Thèse de doctorat université Paris 6 (2007).
  • K. Hamidi, E. Dahia, D. Achour and A. Tallab, Two-Lipschitz operator ideals, Journal of Mathematical Analysis and Applications 491, no. 2...
  • H. Jarchow, Factorization through inclusion mapping between l_p-spaces, Mathematische Annalen 220 (1976), 123-135. https://doi.org/10.1007/BF01351696
  • W. B. Johnson and G. Schechtman, Diamond graphs and super-reflexivity, J. Topol. Anal. 1, no. 2 (2009), 177-189. https://doi.org/10.1142/S1793525309000114
  • M. Kim, The ideal of weakly $ p$-nuclear operators and its injective and surjective hulls, J. Korean Math. Soc. 56 (2019), 225-237.
  • L. Mezrag and A. Tallab, On Lipschitz $tau(p)$-summing operators, Colloq Math. 147 (2017), 95-114. https://doi.org/10.4064/cm6763-3-2016
  • D. Pellegrino, P. Rueda and E. A. Sánchez-Pérez, Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials,...
  • A. Pietsch, l_p-faktorisierbare operatorn in Banach-Räumen, Acta Sci. Math. (Szeged) 31 (1970), 117-123.
  • D. P. Sinha and A. K. Karn, Compact operators whose adjoints factor through subspaces of l_p, Studia Math. 151 (2002), 17-33. https://doi.org/10.4064/sm150-1-3
  • T. Toufik and D. Achour, The ideal of Lipschitz classical p-compact operators and its injective hull, Moroccan J. of Pure and Appl. Anal....
  • P. Turco and R. Villafañe, Galois connection between Lipschitz and linear operator ideals and minimal Lipschitz operator ideals, Journal of...
  • N. Weaver, Lipschitz Algebras, World Scientific Publishing Co. Singapore (1999). https://doi.org/10.1142/4100
  • Y. Rachid, Certaines classes d'opérateurs générés par une procédure d'interpolation, Ph.D. thesis. University of Mohamed Boudiaf,...
  • R. Yahi, D. Achour, P. Rueda, Absolutely summing Lipschitz conjugates, Mediterr. J. Math. 13 (2016), 1949-1961. https://doi.org/10.1007/s00009-015-0623-2