The extension of two-Lipschitz operators

Elhadj Dahia

doi:10.4995/agt.2024.20296

Authors

Elhadj Dahia Université de M'Sila https://orcid.org/0000-0001-7206-0115

DOI:

https://doi.org/10.4995/agt.2024.20296

Keywords:

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

Abstract

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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