We introduce and study the Lipschitz injective hull of Lipschitz operator ideals defined between metric spaces. We show some properties and apply the results to the ideal of Lipschitz p-nuclear operators, obtaining the ideal of Lipschitz quasi p-nuclear operators. Also, we introduce in a natural way the ideal of Lipschitz Pietsch p-integral operators and show that its Lipschitz injective hull coincide with the ideal of Lipschitz p-summing operators defined by Farmer and Johnson. Finally, we consider both ideals as Lipschitz operator ideals between a metric space and a Banach space, showing that these ideals are not of composition type. Their maximal hull and minimal kernel are also studied.

中文翻译：

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Lipschitz 算子的 Lipschitz 内射壳的理想和应用

我们介绍并研究了在度量空间之间定义的 Lipschitz 算子理想的 Lipschitz 内射壳。我们展示了一些性质并将结果应用于 Lipschitz p 核算子的理想，获得 Lipschitz 准 p 核算子的理想。此外，我们以自然的方式引入了 Lipschitz Pietsch p 积分算子的理想，并表明其 Lipschitz 单射包与 Farmer 和 Johnson 定义的 Lipschitz p 求和算子的理想一致。最后，我们将这两个理想都视为度量空间和 Banach 空间之间的 Lipschitz 算子理想，表明这些理想不是复合类型的。还研究了它们的最大外壳和最小内核。