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arXiv · 2204.08738

On locally finite dimensional traces

Massoud Amini·Mehdi Moradi
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Abstract

We partially resolve three open questions on approximation properties of traces on simple C*-algebras. We partially answer two questions raised by Nate Brown by showing that locally finite dimensional (LFD) traces form a convex set on simple C*-algebras and that they are automatically uniformly LFD on locally reflexive C*-algebras. We prove that all the traces on the reduced \C-algebra $C^*_r(\Gamma)$ of a discrete amenable ICC group $\Gamma$ are uniformly LFD, and conclude that $C^*_r(\Gamma)$ is strong-NF in the sense of Blackadar-Kirchberg in this case. This partially answers another open question raised by Brown.

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Massoud Amini, Mehdi Moradi. 2022-04-19. On locally finite dimensional traces. https://arxiv.org/abs/2204.08738

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