Algebra · Oct 6, 2026

Relative bicentralizers and modular spectral recovery

Proves Connes' bicentralizer conjecture for every type III1 factor with separable predual and every faithful normal state. More generally, for every inclusion

N\subset M

of von Neumann algebras with separable preduals admitting a faithful normal conditional expectation, constructs an amenable expected subalgebra

P\subset N

with

P'\cap c(M)=N'\cap c(M)

, resolving the relative bicentralizer conjecture.

Contributors

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Sources

openai/math catalogue entry ↗
Formalization scope note ↗