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arXiv · 2501.12341

Lip-Linear operators and their connection to Lipschitz tensor products

Athmane Ferradi·Khalil Saadi
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Abstract

The linear operators defined on the Lipschitz projective tensor product of X and E motivate the study of a distinct class of operators acting on the cartesian produc X E. This class, denoted by LipL(X E;F), combines Lipschitz and linear properties, forming an intermediate framework between bilinear operators and two-Lipschitz operators. We establish an identification between this space and L(X E;F), which also links it to the space of bilinear operators B(AE(X) E;F). Furthermore, we extend summability concepts within this category, with a particular focus on integral and dominated (p;q)-summing operators

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Athmane Ferradi, Khalil Saadi. 2025-01-21. Lip-Linear operators and their connection to Lipschitz tensor products. https://arxiv.org/abs/2501.12341

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