The extension of two-Lipschitz operators




two-Lipschitz operator, compact two-Lipschitz operator, extension of two-Lipschitz operator


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.


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Author Biography

Elhadj Dahia, Université de M'Sila

Laboratoire de Matèmatiques et Physique Appliquées, École Normale Supérieure de Bousaada (Algeria) ; Laboratoire d’Analyse Fonctionnelle et Géométrie des Espaces, University of M’sila (Algeria)


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How to Cite

E. Dahia, “The extension of two-Lipschitz operators”, Appl. Gen. Topol., vol. 25, no. 1, pp. 47–56, Apr. 2024.



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