An ultrapower construction of the multiplier algebra of a C*-algebra with an application to boundary amenability of groups

Abstract

Using ultrapowers of C-algebras, we provide a new construction of the multiplier algebra of a C-algebra. This extends the work of Avsec and Goldbring [Houston J. Math., to appear, arXiv:1610.09276] to the setting ofnoncommutative and nonseparable C-algebras. We also extend their work to give a new proof of the fact that groups acting transitively on locally finite trees with boundary amenable stabilizers are boundary amenable.