REVIEW 1 cited by
Haagerup and St{o}rmer's conjecture for pointwise inner automorphisms
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Haagerup and St{o}rmer's conjecture for pointwise inner automorphisms
read the original abstract
In 1988, Haagerup and St{\o}rmer conjectured that any pointwise inner automorphism of a type $\rm III_1$ factor is a composition of an inner and a modular automorphism. We study this conjecture and prove that any type $\rm III_1$ factor with trivial bicentralizer indeed satisfies this condition. In particular, this shows that Haagerup and St{\o}rmer's conjecture holds in full generality if Connes' bicentralizer problem has an affirmative answer. Our proof is based on Popa's intertwining theory and Marrakchi's recent work on relative bicentralizers.
Forward citations
Cited by 1 Pith paper
-
Ergodicity of the bicentralizer flow and Kadison's problem
Ergodicity of the relative bicentralizer flow for type III₁ irreducible subfactors with expectation implies they contain maximal abelian subalgebras, completing Kadison's problem.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.