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<p>We prove that every bilinear Lipschitz map—Lipschitz in the metric space variable <i>X</i> and linear in the Banach space variable <i>E</i>—can be expressed as the composition of a canonical two-Lipschitz map with a bounded linear operator. Moreover, this correspondence induces an isometric isomorphism between the space of such two-Lipschitz mappings and the space of bounded linear operators. As applications, we establish results for composition ideals of two-Lipschitz operators, including Cohen strongly two-Lipschitz <i>p</i>-summing, two-Lipschitz factorable strongly <i>p</i>-summing and two-Lipschitz factorable strongly <i>p</i>-nuclear operators.</p>

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Tensor Representations of Two-Lipschitz Operator Ideals by Trace Duality

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Dahmane Achour,
  • Elhadj Dahia,
  • Khaled Hamidi,
  • Abdelhamid Tallab

摘要

We prove that every bilinear Lipschitz map—Lipschitz in the metric space variable X and linear in the Banach space variable E—can be expressed as the composition of a canonical two-Lipschitz map with a bounded linear operator. Moreover, this correspondence induces an isometric isomorphism between the space of such two-Lipschitz mappings and the space of bounded linear operators. As applications, we establish results for composition ideals of two-Lipschitz operators, including Cohen strongly two-Lipschitz p-summing, two-Lipschitz factorable strongly p-summing and two-Lipschitz factorable strongly p-nuclear operators.