Ideals in the Roe algebras of discrete metric spaces with coefficients in \(\mathcal B(H)\) (Q1044800)

Let \(X\) be a discrete metric space with bounded geometry. In a series of papers, \textit{X.-M.\thinspace Chen} and \textit{Q.\,Wang} have studied the ideal structure of the Roe algebras associated to \(X\). In particular, they characterized the ideals of the Roe algebra \(C^*(X)\) and the uniform Roe algebra \(C_u^*(X)\) in the case \(X\) satisfies the Yu property (A) [J.~Funct.\ Anal.\ 216, 191--211 (2004; Zbl 1066.46056)] and [Bull.\ Lond.\ Math.\ Soc.\ 38, 847--856 (2006; Zbl 1114.46049)]. Let \(H \) be a separable Hilbert space and \(C^*(X,\mathcal {B}(H))\) be the Roe algebra of \(X\) with coefficients in \(\mathcal{B}(H)\). In the paper under review, the authors introduce the notion of ideal family of weighted subspaces of \(X\). They show that, if \(X\) satisfies the Yu property (A), then the ideals of the Roe algebra \(C^*(X,{\mathcal B}(H))\) are characterized by the ideal families of weighted subspaces of \(X\).