A Schur-Horn theorem in II$_1$ factors

Abstract

Given a II 1 factor M and a diffuse abelian von Neumann subalgebra A ⊂ M, we prove a version of the Schur-Horn theorem, namelywhere ≺ denotes spectral majorization, E A the unique trace-preserving conditional expectation onto A, and U M (b) the unitary orbit of b in M.This result is inspired by a recent problem posed by Arveson and Kadison.

Identifiers

DOI

10.1512/iumj.2007.56.3113

Citations and references