Uniformly bounded representations of discrete measured groupoid into finite Von Neumann algebras

Alessio Savini

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arXiv · 2512.21442

Uniformly bounded representations of discrete measured groupoid into finite Von Neumann algebras

Alessio Savini

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Abstract

Let $(\mathcal{G},\nu)$ be a $t$-discrete ergodic groupoid. Consider a finite Von Neumann algebra $\mathcal{M}$ with separable predual. We prove that every uniformly bounded measurable representation $\rho:\mathcal{G} \rightarrow \mathrm{GL}(\mathcal{M})$ into the invertible elements of $\mathcal{M}$ is similar to a unitary representation.

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Alessio Savini. 2025-12-24. Uniformly bounded representations of discrete measured groupoid into finite Von Neumann algebras. https://arxiv.org/abs/2512.21442

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