An interpolative class of two-Lipschitz mappings of composition type

• Hamidi, Khaled ^[1] ; Tallab, Abdelhamid ^[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. 2, 2024, págs. 475-489
• Idioma: inglés
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• Resumen

  • The paper deals with some further results concerning the class of two-Lipschitz operators. We prove first an isometric isomorphismidentification of two-Lipschitz operators and Lipschitz operators. After defining and characterizing the adjoint of a two-Lipschitz operator, we prove a Schauder type theorem on the compactness of the adjoint. We study the extension of two-Lipschitz operators from the 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 the cartesian product of two pointed metric spaces admits an extension with the same two-Lipschitz norm under some requirements on domaine spaces.