On the equi-nuclearity of Roe algebras of metric spaces

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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