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On the Equi-nuclearity of Roe Algebras of Metric Spaces |
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| Authors: | Xiaoman CHEN Benyin FU and Qin WANG |
| Institution: | 1. School of Mathernatical Sciences,Fudan University,Shanghai 200433,China 2. School of Mathematical Sciences,Fudan University,Shanghai 200433,China 3. Department of Applied Mathematics,Donghua University,Shanghai 200051,China |
| Abstract: | The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {X i } i=1∞, if {C u *(X i )} i=1∞ are equi-nuclear and under some proper gluing conditions, it is proved that C u *(X) is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C*(X) is not nuclear. |
| Keywords: | Nuclear C*-algebra Uniform Roe algebra Equi-nuclear uniform Roe algebra |
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