Strict comparison holds in the uniform Roe algebra of a discrete amenable group

George A. Elliott, Chun Guang Li, Zhuang Niu +1

Let $\Gamma$ be a countable discrete amenable group, and let $A=l^{\infty }(\Gamma )⋊\Gamma$. It is shown that if $a,b\in A\otimes \mathcal{K}$ are positive elements such that $$\mathrm{d}_…