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arXiv · 2603.22049

Sublinear growth of 1-cocycles and uniform convexity

Andreas Thom
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Abstract

Let G be a finitely generated group, let $\pi \colon G \to {\rm GL}(E)$ be a uniformly bounded $c_0$-representation on a superreflexive Banach space $E$, and let $b \colon G \to E$ be a $1$-cocycle for $\pi$. Then $b$ has sublinear growth with respect to the word length. As a corollary we obtain the corresponding Hilbert space statement for strongly mixing unitary representations.

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Andreas Thom. 2026-03-23. Sublinear growth of 1-cocycles and uniform convexity. https://arxiv.org/abs/2603.22049

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