Operator algebraic approach to inverse and stability theorems for amenable groups

Marcus De Chiffre, Narutaka Ozawa, Andreas Thom

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 wit…