A Schur-Horn Theorem in II_1 factors

MARTIN ARGERAMI; PEDRO MASSEY

INDIANA UNIVERSITY MATHEMATICS JOURNAL

INDIANA UNIVERSITY

Año: 2007 vol. 56 p. 2051 - 2059

0022-2518

Given a II_1 factor M and a diffuse abelian von Neumann subalgebra A of M, we prove a version of the Schur-Horn theorem, namely that the sigma-weak closure of the values of image under the trace preserving conditional expectation onto A of the unitray orbit of a self-adjoint element b of M coincides with the set of self-adjoint operators of A that are majorized by b (in the sense of E. Kamei). This result is inspired by a recent problem posed by Arveson and Kadison.