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Autumn 2019 An ultrapower construction of the multiplier algebra of a $C^*$-algebra‎ ‎and an application to boundary amenability of groups
Facundo Poggi, Román Sasyk
Adv. Oper. Theory 4(4): 852-864 (Autumn 2019). DOI: 10.15352/aot.1904-1501

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 acting transitively on locally finite trees with boundary amenable stabilizers are‎ ‎boundary amenable‎.

Citation

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Facundo Poggi. Román Sasyk. "An ultrapower construction of the multiplier algebra of a $C^*$-algebra‎ ‎and an application to boundary amenability of groups." Adv. Oper. Theory 4 (4) 852 - 864, Autumn 2019. https://doi.org/10.15352/aot.1904-1501

Information

Received: 30 April 2019; Accepted: 11 May 2019; Published: Autumn 2019
First available in Project Euclid: 15 May 2019

zbMATH: 07064110
MathSciNet: MR3949980
Digital Object Identifier: 10.15352/aot.1904-1501

Subjects:
Primary: 46L05
Secondary: 03C20, 20F65

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.4 • No. 4 • Autumn 2019
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