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Uniformly quasi-Hermitian groups are supramenable
Part of
- Selfadjoint operator algebras
- Abstract harmonic analysis
Mahmud Azam, Ebrahim Samei
Journal:

Canadian Mathematical Bulletin / Volume 65 / Issue 3 / September 2022

Published online by Cambridge University Press:

14 July 2021, pp. 665-673

Print publication:

September 2022
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Motivated by the recent result in Samei and Wiersma (2020, Advances in Mathematics 359, 106897) that quasi-Hermitian groups are amenable, we consider a generalization of this property on discrete groups associated to certain Roe-type algebras; we call it uniformly quasi-Hermitian. We show that the class of uniformly quasi-Hermitian groups is contained in the class of supramenable groups and includes all subexponential groups. We also show that they are invariant under quasi-isometry.

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Uniformly quasi-Hermitian groups are supramenable