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arXiv · 2601.19355

Equivalences between certain properties of weighted Lipschitz operators

Mathis Lemay
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Abstract

We show that for a weighted Lipschitz operator $\omega\widehat{f}$, certain linear properties are equivalent. Specifically, we prove that compactness, strict singularity, and strict cosingularity are all equivalent to the property of not fixing any complemented copy of $\ell^1$. Then we generalize this result to operators between Lipschitz-free spaces that preserve finitely supported elements, a larger class of operators.

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Mathis Lemay. 2026-01-27. Equivalences between certain properties of weighted Lipschitz operators. https://arxiv.org/abs/2601.19355

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