English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In 1988, Haagerup and St{\o}rmer conjectured that any pointwise innerautomorphism of a type $\rm III_1$ factor is a composition of an inner and amodular automorphism. We study this conjecture and prove that any type $\rmIII_1$ factor with trivial bicentralizer indeed satisfies this condition. Inparticular, this shows that Haagerup and St{\o}rmer's conjecture holds in fullgenerality if Connes' bicentralizer problem has an affirmative answer. Ourproof is based on Popa's intertwining theory and Marrakchi's recent work onrelative bicentralizers.

Haagerup and St{\o}rmer's conjecture for pointwise inner automorphisms