2 results
Co-spectral radius of intersections
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems / Volume 44 / Issue 2 / February 2024
- Published online by Cambridge University Press:
- 17 April 2023, pp. 509-523
- Print publication:
- February 2024
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- Article
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We study the behavior of the co-spectral radius of a subgroup H of a discrete group
$\Gamma $ under taking intersections. Our main result is that the co-spectral radius of an invariant random subgroup does not drop upon intersecting with a deterministic co-amenable subgroup. As an application, we find that the intersection of independent co-amenable invariant random subgroups is co-amenable.
A Homological Property and Arens Regularity of Locally Compact Quantum Groups
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- Journal:
- Canadian Mathematical Bulletin / Volume 60 / Issue 1 / 01 March 2017
- Published online by Cambridge University Press:
- 20 November 2018, pp. 122-130
- Print publication:
- 01 March 2017
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- Article
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We characterize two important notions of amenability and compactness of a locally compact quantum group
$\mathbb{G}$ in terms of certain homological properties. For this, we show that $\mathbb{G}$ is character amenable if and only if it is both amenable and co-amenable. We finally apply our results to Arens regularity problems of the quantum group algebra 
${{L}^{1}}\left( \mathbb{G} \right)$. In particular, we improve an interesting result by Hu, Neufang, and Ruan.
