On uniform Hilbert Schmidt stability of groups
Abstract
A group $\Gamma$ is said to be uniformly HS stable if any map $\varphi : \Gamma \to U(n)$ that is almost a unitary representation (w.r.t. the Hilbert Schmidt norm) is close to a genuine unitary representation of the same dimension. We present a complete classification of uniformly HS stable groups among finitely generated residually finite ones. Necessity of the residual finiteness assumption is discussed. A similar result is shown to hold assuming only amenability.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.10304
- arXiv:
- arXiv:2010.10304
- Bibcode:
- 2020arXiv201010304A
- Keywords:
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- Mathematics - Group Theory
- E-Print:
- 10 pages. Revised introduction and references. To appear in Proceedings of the American Mathematical Society