OPERATOR ALGEBRAIC APPROACH TO INVERSE AND STABILITY THEOREMS FOR AMENABLE GROUPS Article Swipe

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Marcus De Chiffre , Narutaka Ozawa , Andreas Thom ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.1112/s0025579318000335 · OA: W2626858973

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