Ideals in the Roe algebras of discrete metric spaces with coefficients in $\mathcal{B}$(H)

Abstract

The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coefficients in $\mathcal{B}$(H) is completely characterized by the ideal families of weighted subspaces of X, where $\mathcal{B}$(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.

Keywords

Roe algebra / Ideal / Metric space / Coarse geometry / Band-dominated operator

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