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. (Lean)

Manuscripts (2)

Expected amenable subalgebras preserving core commutants

September 23, 2026 · source · cite as \cite{OAI:Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026}

We prove that every inclusion N\subset M of von Neumann algebras with separable preduals and a faithful normal conditional expectation contains an expected amenable subalgebra P\subset N such that P'\cap c(M)=N'\cap c(M), where c(M) denotes the continuous core of M. This resolves the relative bicentralizer conjecture in this setting.

Bounded recovery for modular spectral averages

September 23, 2026 · source · Lean formalization available · cite as \cite{OAI:Bounded-recovery-for-modular-spectral-averages-September-23-2026}

We prove a bounded spectral recovery theorem for a von Neumann algebra with a faithful normal state whose centralizer consists only of scalars. A positive averaged squared norm for an arbitrary bounded Hilbert-space operator on shrinking modular spectral bands can be recovered on uniformly bounded algebra elements with shrinking spectral support. We apply this theorem to spectral intertwining rigidity and obtain an alternative proof of bicentralizer triviality for type III₁ factors with separable predual.

Result 290 · Operator algebras. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.