English

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

Operator Algebras 2026-05-04 v2

Abstract

We introduce the notion of selfless W^*-probability space and study its connection with Connes' bicentralizer problem. In particular, we show that if MM is a separable type III1{\rm III_1} factor with trivial bicentralizer, then (M,φ)(M, \varphi) is selfless for every faithful normal state φM\varphi \in M_\ast.

Cite

@article{arxiv.2511.11409,
  title  = {Selfless W$^*$-probability spaces and Connes' bicentralizer problem},
  author = {Cyril Houdayer and Amine Marrakchi},
  journal= {arXiv preprint arXiv:2511.11409},
  year   = {2026}
}

Comments

5 pages. To appear in J. Math. Soc. Japan

R2 v1 2026-07-01T07:37:39.352Z