The extension of two-Lipschitz operators

• Dahia, Elhadj ^[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. 47-56
• Idioma: inglés
• DOI: 10.4995/agt.2024.20296
• Enlaces
  • Texto completo
• Resumen

  • The paper deals with some further results concerning the class of two-Lipschitz operators. We prove first an isometric isomorphism identification of two-Lipschitz operators and Lipschitz operators. After defining and characterize the adjoint of two-Lipschitz operator, we prove a Schauder type theorem on the compactness of the adjoint. We study the extension of two-Lipschitz operators from cartesian product of two complemented subspaces of a Banach space to the cartesian product of whole spaces. Also, we show that every two-Lipschitz functional defined on cartesian product of two pointed metric spaces admits an extension with the same two-Lipschitz norm, under some requirements on domaine spaces.

• Referencias bibliográficas
  • D. Achour, E. Dahia, and M. A. S. Saleh. Multilinear mixing operators and Lipschitz mixing operator ideals, Operators and Matrices 12, no....
  • D. Achour, E. Dahia, and P. Turco, The Lipschitz injective hull of Lipschitz operator ideals and applications, Banach J. Math. Anal. 14 (2020),...
  • D. Achour, E. Dahia, and P. Turco, Lipschitz p-compact mappings, Monatshefte für Mathematik 189 (2019), 595-609. https://doi.org/10.1007/s00605-018-1252-1
  • D. Achour, P. Rueda, E.A. Sánchez-Pérez, and R. Yahi, Lipschitz operator ideals and the approximation property, J. Math. Anal. Appl. 436 (2016),...
  • R. F. Arens and J. Jr. Eells, On embedding uniform and topological spaces, Pacific J. Math 6 (1956), 397-403. https://doi.org/10.2140/pjm.1956.6.397
  • Y. Benyamini and J. Lindenstrauss. Geometric nonlinear functional analysis, vol. 1, Amer. Math. Soc. Colloq. Publ., vol. 48, Amer. Math. Soc.,...
  • E. Dahia, and K. Hamidi, Lipschitz integral operators represented by vector measures, Appl. Gen. Topol. 22, no. 2 (2021), 367-383. https://doi.org/10.4995/agt.2021.15061
  • A. Defant and K. Floret, Tensor norms and operator ideals, North-Holland, Amsterdam, 1992.
  • M. Dubei, E. D. Tymchatynb, and A. Zagorodnyuk, Free Banach spaces and extension of Lipschitz maps, Topology 48 (2009), 203-212. https://doi.org/10.1016/j.top.2009.11.020
  • K. Hamidi, E. Dahia, D. Achour, and A. Tallab, Two-Lipschitz operator ideals, J. Math. Anal. Appl. 491 (2020), Paper no. 124346. https://doi.org/10.1016/j.jmaa.2020.124346
  • T. L. Hayden, The extension of bilinear functionals, Pacific J. Math. 22 (1967), 99-108. https://doi.org/10.2140/pjm.1967.22.99
  • M. S. Ramanujan, and E. Schock, Operator ideals and spaces of bilinear operators, Lin. Multilin. Alg. 18 (1985), 307-318. https://doi.org/10.1080/03081088508817695
  • D. Ruch, Characterizations of compact bilinear maps, Lin. Multilin. Alg. 25 (1989), 297-307. https://doi.org/10.1080/03081088908817956
  • E. A. Sánchez-Pérez, Product spaces generated by bilinear maps and duality, Czechoslovak Mathematical Journal 65 (2015), 801-817. https://doi.org/10.1007/s10587-015-0209-y
  • I. Sawashima, Methods of Lipschitz duals, Lecture Notes in econom. and Math. systems, vol. 419, Springer Verlag, 1975, pp. 247-259.
  • N. Weaver. Lipschitz Algebras, World Scientific Publishing Co., Singapore, 1999. https://doi.org/10.1142/4100