English

Amenable absorption in amalgamated free product von Neumann algebras

Operator Algebras 2019-01-09 v3

Abstract

We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras M=M1BM2M = M_1 \ast_B M_2. Our main result states that under natural analytic assumptions, any amenable subalgebra of MM that has a large intersection with M1M_1 is actually contained in M1M_1. The proof does not rely on Popa's asymptotic orthogonality property but on the study of non normal conditional expectations.

Keywords

Cite

@article{arxiv.1606.00808,
  title  = {Amenable absorption in amalgamated free product von Neumann algebras},
  author = {Rémi Boutonnet and Cyril Houdayer},
  journal= {arXiv preprint arXiv:1606.00808},
  year   = {2019}
}

Comments

8 pages. To appear in Kyoto J. Math