$K$-theory of ghostly ideals for $\ell^p$-coarsely embeddable spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912880512729088 |
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| author | Guo, Liang Li, Kang Wang, Qin |
| author_facet | Guo, Liang Li, Kang Wang, Qin |
| contents | Ghostly ideals are among the most mysterious objects in coarse index theory. In this paper, we show that if a metric space $X$ with bounded geometry admits a coarse embedding into an $\ell^p$-space ($1 \le p < \infty$), then the canonical inclusion from any geometric ideal to the corresponding ghostly ideal induces an isomorphism in $K$-theory. As consequences, we deduce that such spaces satisfy the relative coarse Baum-Connes conjectures, as well as the operator norm localization property for finite rank projections ($ONL_{\mathcal P_{Fin}}$). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_22438 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $K$-theory of ghostly ideals for $\ell^p$-coarsely embeddable spaces Guo, Liang Li, Kang Wang, Qin K-Theory and Homology Functional Analysis Operator Algebras 19K56, 47L20 Ghostly ideals are among the most mysterious objects in coarse index theory. In this paper, we show that if a metric space $X$ with bounded geometry admits a coarse embedding into an $\ell^p$-space ($1 \le p < \infty$), then the canonical inclusion from any geometric ideal to the corresponding ghostly ideal induces an isomorphism in $K$-theory. As consequences, we deduce that such spaces satisfy the relative coarse Baum-Connes conjectures, as well as the operator norm localization property for finite rank projections ($ONL_{\mathcal P_{Fin}}$). |
| title | $K$-theory of ghostly ideals for $\ell^p$-coarsely embeddable spaces |
| topic | K-Theory and Homology Functional Analysis Operator Algebras 19K56, 47L20 |
| url | https://arxiv.org/abs/2511.22438 |