On coarse geometry of separable dual Banach spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915654893830144 |
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| author | Jackson, Stephen Krause, Cory Sari, Bunyamin |
| author_facet | Jackson, Stephen Krause, Cory Sari, Bunyamin |
| contents | We study the obstructions to coarse universality in separable dual Banach spaces. We prove coarse non-universality of several classes of dual spaces, including those with conditional spreading bases, as well as generalized James and James tree spaces. We also give quantitative counterparts of some of the results, clarifying the distinction between coarse non-universality and the non-equi-coarse embeddings of the Kalton graphs. Unique to our approach is the use of a Ramsey ultrafilter. While the existence of such ultrafilters typically requires $\mathsf{CH}$, we are able to show that the conclusions of our theorems follow from $\mathsf{ZFC}$, alone via an absoluteness argument. Finally, we also show how our techniques can be used to prove various previously known results in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01561 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On coarse geometry of separable dual Banach spaces Jackson, Stephen Krause, Cory Sari, Bunyamin Functional Analysis 46B85, 46B06 We study the obstructions to coarse universality in separable dual Banach spaces. We prove coarse non-universality of several classes of dual spaces, including those with conditional spreading bases, as well as generalized James and James tree spaces. We also give quantitative counterparts of some of the results, clarifying the distinction between coarse non-universality and the non-equi-coarse embeddings of the Kalton graphs. Unique to our approach is the use of a Ramsey ultrafilter. While the existence of such ultrafilters typically requires $\mathsf{CH}$, we are able to show that the conclusions of our theorems follow from $\mathsf{ZFC}$, alone via an absoluteness argument. Finally, we also show how our techniques can be used to prove various previously known results in the literature. |
| title | On coarse geometry of separable dual Banach spaces |
| topic | Functional Analysis 46B85, 46B06 |
| url | https://arxiv.org/abs/2501.01561 |