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

Document Type: Original Article

Authors

University of Buenos Aires, Argentina.

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 of noncommutative and non separable $C^*$-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.

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