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OPERATOR ALGEBRAIC APPROACH TO INVERSE AND STABILITY THEOREMS FOR AMENABLE GROUPS
Published online by Cambridge University Press: 30 August 2018
Abstract
We prove an inverse theorem for the Gowers $U^{2}$-norm for maps
$G\rightarrow {\mathcal{M}}$ from a 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
$\unicode[STIX]{x1D700}$-representations
$G\rightarrow {\mathcal{U}}({\mathcal{M}})$ with respect to
$\Vert \cdot \Vert$.
MSC classification
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- Research Article
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- Copyright © University College London 2018
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