The extension of two-Lipschitz operators
Submitted: 2023-09-08
|Accepted: 2023-12-01
|Published: 2024-04-02
Copyright (c) 2024 Elhadj Dahia
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
two-Lipschitz operator, compact two-Lipschitz operator, extension of two-Lipschitz operator
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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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