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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.19355 |
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| _version_ | 1866915885528121344 |
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| author | Lemay, Mathis |
| author_facet | Lemay, Mathis |
| contents | We show that for a weighted Lipschitz operator $ω\widehat{f}$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19355 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivalences between certain properties of weighted Lipschitz operators Lemay, Mathis Functional Analysis We show that for a weighted Lipschitz operator $ω\widehat{f}$, 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. |
| title | Equivalences between certain properties of weighted Lipschitz operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2601.19355 |