Geodesic
Hilbert $C^*$-modules related to discrete metric spaces
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 55-63

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It is shown that a metric on the union of the sets $X$ and $Y$ determines a Hilbert $C^*$-module over the uniform Roe algebra of the space $X$. Several examples of such Hilbert $C^*$-modules are described in detail.
Keywords: metric space, Roe algebra, $C^*$-algebra, Hilbert $C^*$-module. 
@article{IVM_2021_5_a7,
     author = {V. M. Manuilov},
     title = {Hilbert $C^*$-modules related to discrete metric spaces},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {55--63},
     publisher = {mathdoc},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_5_a7/}
}
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V. M. Manuilov. Hilbert $C^*$-modules related to discrete metric spaces. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2021), pp. 55-63. http://geodesic.mathdoc.fr/item/IVM_2021_5_a7/