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Uniformly quasi-Hermitian groups are supramenable

Part of: Selfadjoint operator algebras Abstract harmonic analysis

Published online by Cambridge University Press:  14 July 2021

Mahmud Azam  and
Ebrahim Samei
Mahmud Azam
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SKS7N 5E6, Canada e-mail: [email protected]
Ebrahim Samei*
Affiliation:
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SKS7N 5E6, Canada e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

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.

Keywords

Qausi-Hermitian groupsamenable groupssupramenable groupsgroups with subexponential growthuniform Roe algebras

MSC classification

Primary: 43A20: $L^1$-algebras on groups, semigroups, etc.
Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 46L55: Noncommutative dynamical systems
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 3 , September 2022 , pp. 665 - 673
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

The first-named author was partially supported by NSERC USRA 2020. The second-named author was partially support by NSERC Grant no. 409364-2019.

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