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

2025/07/06 by Ferradi, Athmane, Saadi, Khalil
#46B28 #47B10 #47L20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2507.04492

Abstract

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 Kwapień. 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.

Citations

• Lip-Linear operators and their connection to Lipschitz tensor products
• The Duality between Ideals of Multilinear Operators and Tensor Norms
• Hyper-ideals of multilinear operators
• Lipschitz tensor product
• Some properties of Lipschitz strongly p-summing operators

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• Galois connection between Lipschitz and linear operator ideals and\n minimal Lipschitz operator ideals