On the equi-nuclearity of Roe algebras of metric spaces

Xiaoman Chen; Benyin Fu; Qin Wang

doi:10.1007/s11401-010-0588-1

On the equi-nuclearity of Roe algebras of metric spaces

Xiaoman Chen
, Benyin Fu
, Qin Wang^*

^*此作品的通讯作者

Fudan University
Donghua University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
页（从-至）	519-528
页数	10
期刊	Chinese Annals of Mathematics. Series B
卷	31
期	4
DOI	https://doi.org/10.1007/s11401-010-0588-1
出版状态	已出版 - 2010
已对外发布	是

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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 \{Xi\}i=1∞, if \{Cu*(Xi)\}i=1 ∞ are equi-nuclear and under some proper gluing conditions, it is proved that Cu*(X) is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C*(X) is not nuclear.",

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AB - 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 {Xi}i=1∞, if {Cu*(Xi)}i=1 ∞ are equi-nuclear and under some proper gluing conditions, it is proved that Cu*(X) is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C*(X) is not nuclear.

KW - Equi-nuclear uniform Roe algebra

KW - Nuclear C-algebra

KW - Uniform Roe algebra

UR - https://www.scopus.com/pages/publications/77955515332

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On the equi-nuclearity of Roe algebras of metric spaces

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