An ultrapower construction of the multiplier algebra of a $C^{\ast }$-algebra and an application to boundary amenability of groups

Abstract

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

v.3: Final version, appeared in Advances in Operator Theory. New title and new section on boundary amenability of groups added to accommodate a request of the referee. In order to improve the exposition, some other small changes were made

References in corpus (1)

• Boundary amenability of groups via ultrapowers