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<p>In this paper, we present and characterize the injective hull of a two-Lipschitz operator ideal 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.</p>

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Building Ideals of Two-Lipschitz Operators Between Metric and Banach Spaces

  • 期刊论文

  • 发表日期：

    2025年2月10日

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  • Dahmane Achour,
  • Elhadj Dahia

摘要

In this paper, we present and characterize the injective hull of a two-Lipschitz operator ideal 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.