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| On the Equi-nuclearity of Roe Algebras of Metric Spaces |
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Citation： |
Xiaoman CHEN,Benyin FU,Qin WANG.On the Equi-nuclearity of Roe Algebras of Metric Spaces[J].Chinese Annals of Mathematics B,2010,31(4):519~528 |
| Page view： 1857
Net amount： 1315 |
Authors： |
Xiaoman CHEN; Benyin FU; Qin WANG; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10731020, 10971023), the
Shu Guang Project of Shanghai Municipal Education Commission and Shanghai Education Department
Foundation (No. 07SG38) and the Foundation of the Ministry of Education of China. |
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| 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
$\{X_i\}_{i=1}^{\infty}$, if $\{C_u^*(X_i)\}_{i=1}^{\infty}$ 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： |
C* -algebra, Uniform Roe algebra, Equi-nuclear uniform Roe algebra |
Classification： |
46L07, 46L80 |
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