A Measurable Selector in Kadison’s Carpenter’s Theorem

Abstract

We show the existence of a measurable selector in Carpenter's Theorem due to Kadison [30,31]. This solves a problem posed by Jasper and the first author in [16]. As an application we obtain a characterization of all possible spectral functions of shift-invariant subspaces of L 2 (R d ) and Carpenter's Theorem for type I ∞ von Neumann algebras.