Building ideals of two-Lipschitz operators between mertic and Banach spaces

2023/12/05 by Dahmane Achour, Achour, Dahmane, Elhadj Dahia +1 · 2 citations
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.2312.03104

Abstract

In this paper, we present and characterize the injective hull of a two-Lipschitz operator ideals and the definition of two-Lipschitz dual operator ideal. Also we introduce two methods for creating ideals of two-Lipschitz operators from a pair of Lipschitz operator ideals. Namely, Lipschitzization and factorization method. We show the closedness, the injectivity and the symmetry of these two-Lipschitz ideals according to the closedness, injectivity and symmetry of the corresponding Lipschitz operator ideals. Some illustrative examples are given.

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• Projection from space of two-Lipschitz operators onto the space of Bilinear maps
• On injective and interpolative procedures for holomorphic Lipschitz ideals

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