Kadison's problem and ergodicity of the bicentralizer flow and

Abstract

We solve Kadison's problem on the existence of maximal abelian subalgebras in irreducible subfactors $N\subset M$ when $N$ is AFD or when $N$ is with expectation in $M$. In the latter case, we first show that the relative bicentralizer flow of a type ${\mathrm{III}}_1$ irreducible subfactor with expectation is always ergodic. This also implies that for every irreducible subfactor with expectation $N\subset M$, there exists an AFD subfactor with expectation $P\subset N$ that is irreducible in $M$.

arXiv comment17 pages. A solution of Kadison's problem for AFD subfactors has been added in the new version