A tautological continuous field of Roe bimodules
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910069621260288 |
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| author | Manuilov, Vladimir |
| author_facet | Manuilov, Vladimir |
| contents | We generalize the notion of a continuous field of C*-algebras to that of Hilbert C*-bimodules. Given a partially ordered set $P$ and a monotonically non-decreasing family of ternary rings of operators (TROs) assigned to the points of $P$, we equip $P$ with a certain zero-dimensional Hausdorff topology and use a certain compactification $γP$ to get the base space for a continuous field of Hilbert C*-bimodules over $γP$.
As a motivating example, we consider the set $D(X,Y)$ of coarse equivalence classes of metrics on the disjoint union of two metric spaces, $X$ and $Y$. Each such class gives rise to a uniform Roe bimodule, a TRO linking the uniform Roe algebras of $X$ and $Y$. The resulting family of TROs is non-decreasing with respect to the natural partial order on $D(X,Y)$ and thus yields a tautological continuous field of Hilbert C*-bimodules over $γD(X,Y)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23366 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A tautological continuous field of Roe bimodules Manuilov, Vladimir Operator Algebras We generalize the notion of a continuous field of C*-algebras to that of Hilbert C*-bimodules. Given a partially ordered set $P$ and a monotonically non-decreasing family of ternary rings of operators (TROs) assigned to the points of $P$, we equip $P$ with a certain zero-dimensional Hausdorff topology and use a certain compactification $γP$ to get the base space for a continuous field of Hilbert C*-bimodules over $γP$. As a motivating example, we consider the set $D(X,Y)$ of coarse equivalence classes of metrics on the disjoint union of two metric spaces, $X$ and $Y$. Each such class gives rise to a uniform Roe bimodule, a TRO linking the uniform Roe algebras of $X$ and $Y$. The resulting family of TROs is non-decreasing with respect to the natural partial order on $D(X,Y)$ and thus yields a tautological continuous field of Hilbert C*-bimodules over $γD(X,Y)$. |
| title | A tautological continuous field of Roe bimodules |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2603.23366 |