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arXiv · 1706.04544

Operator algebraic approach to inverse and stability theorems for amenable groups

Marcus De Chiffre·Narutaka Ozawa·Andreas Thom
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Abstract

We prove an inverse theorem for the Gowers $U^2$-norm for maps $G\to\mathcal M$ from an countable, discrete, amenable group $G$ into a von Neumann algebra $\mathcal M$ equipped with an ultraweakly lower semi-continuous, unitarily invariant (semi-)norm $\Vert\cdot\Vert$. We use this result to prove a stability result for unitary-valued $\varepsilon$-representations $G\to\mathcal U(\mathcal M)$ with respect to $\Vert\cdot \Vert$.

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Marcus De Chiffre, Narutaka Ozawa, Andreas Thom. 2017-06-14. Operator algebraic approach to inverse and stability theorems for amenable groups. https://doi.org/10.1112/s0025579318000335

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