Family 290Operator algebrasLeanNot yet digested

Relative bicentralizers and modular spectral recovery

Proves Connes' bicentralizer conjecture for every type III

_{1}

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.

Manuscripts in this family · 2

Expected amenable subalgebras preserving core commutants

Sep 23, 2026·Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026.pdf

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.

Full abstract

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Bounded recovery for modular spectral averages

Sep 23, 2026·Bounded-recovery-for-modular-spectral-averages-September-23-2026.pdfLean

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 III

_{1}

factors with separable predual.

Full abstract

PDF on GitHub LaTeX source