标题： Lip-线性算子的复合理想和希尔伯特空间表征 显示英文标题

标题： Composition ideals of Lip-Linear operators and a Hilbert space characterization

摘要： 在本文中，我们研究了使用组合理想方法构造的Lip-线性算子类。 我们关注两个基本的线性算子理想，$p$-求和算子和强$p$-求和算子，并将其扩展以定义相应的Lip-线性算子类。 建立了几个关键结果，包括最初由Kwapień提出的Hilbert空间的特征定理。 具体而言，我们证明了一个Banach空间$F$与Hilbert空间同构当且仅当每个取值于$F$的可分解强$p$-求和Lip-线性算子都是Cohen强$p$-求和的。 显示英文摘要

摘要： In this paper, we investigate classes of Lip-linear operators constructed using the composition ideal method. We focus on two fundamental linear operator ideals, $p$-summing and strongly $p$-summing operators, and extend them to define the corresponding classes of Lip-linear operators. Several key results are established, including a characterization theorem for Hilbert spaces originally due to Kwapie\'{n}. Specifically, we show that a Banach space $F$ is isomorphic to a Hilbert space if and only if every factorable strongly $p$-summing Lip-linear operator with values in $F$ is Cohen strongly $p$-summing.