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.
released 2026-09-23 | 3 theorems · 3 lemmas · 9 proofs · 7,725 words |
PLAY LEVEL 1 »(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.
released 2026-09-23 | 3 theorems · 8 lemmas · 12 proofs · 5,814 words |
PLAY LEVEL 2 »(pdf)
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.