An interpolative class of two-Lipschitz mappings of composition type
Submitted: 2024-01-31
|Accepted: 2024-04-19
|Published: 2024-10-01
Copyright (c) 2024 Khaled Hamidi, Abdelhamid Tallab
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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Keywords:
strongly two-Lipschitz p-summing, two-Lipschitz operator ideal, strongly (p,σ)-continuous, Pietsch domination theorem
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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 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.
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