3 papers
math.OA2026
Ultrapowers of spectral subspaces
Hiroshi Ando, Isaac Goldbring
We prove, for any W-probability space where is a type factor, any nontrivial, proper closed , and any nonprincipal ultrafil…
math.OA2026
Model theory and Connes' bicentralizer problem
Hiroshi Ando, Isaac Goldbring
We make a series of model-theoretic contributions to Connes' bicentralizer problem, one of the most prominent open problems in the theory of von Neumann algebras. Our work builds o…
math.SP2025
A nonstandard approach to the direct integral version of the Spectral Theorem
Isaac Goldbring, Fabrice Nonez
We use nonstandard methods to prove the direct integral version of the Spectral Theorem for Unbounded Self-adjoint Operators. Our proof avoids the standard reduction to the case of…