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Operator algebraic approach to inverse and stability theorems for amenable groups. (arXiv:1706.04544v2 [math.OA] UPDATED)
来源于:arXiv
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 $\Vert\cdot \Vert$. 查看全文>>