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arXiv · 2508.20061

Frame Vector Group Representations and Amenability Properties

Dorin Ervin Dutkay·Catalin Georgescu·Gabriel Picioroaga
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Abstract

We provide a new characterization of amenability for countable groups, based on frame representations admitting almost invariant vectors. By relaxing the frame inequalities, thereby weakening amenability, we obtain a large class of countable groups which we call {\it framenable}. We show that this class has some permanence properties, stands in contrast with property (T), and contains, for example, all free groups $\mathbb{F}_n$, $\textup{Aut}(\mathbb{F}_2)$ and $\textup{Aut}(\mathbb{F}_3)$, all (countable) lattices of $SL(2,\mathbb{R})$, the Baumslag-Solitar groups $BS_{p,q}$, the braid groups $B_n$, and Thompson's group $F$.

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Dorin Ervin Dutkay, Catalin Georgescu, Gabriel Picioroaga. 2025-12-02. Frame Vector Group Representations and Amenability Properties. https://arxiv.org/abs/2508.20061

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