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arXiv · 2511.11409

Selfless W$^*$-probability spaces and Connes' bicentralizer problem

Cyril Houdayer·Amine Marrakchi
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Abstract

We introduce the notion of selfless W$^*$-probability space and study its connection with Connes' bicentralizer problem. In particular, we show that if $M$ is a separable type ${\rm III_1}$ factor with trivial bicentralizer, then $(M, \varphi)$ is selfless for every faithful normal state $\varphi \in M_\ast$.

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Cyril Houdayer, Amine Marrakchi. 2025-11-14. Selfless W$^*$-probability spaces and Connes' bicentralizer problem. https://arxiv.org/abs/2511.11409

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