A contractive version of a Schur-Horn theorem in II1 factors

Abstract

We prove a contractive version of the Schur-Horn theorem for submajorization in II₁ factors that complements some previous results on the Schur-Horn theorem within this context. We obtain a reformulation of a conjecture of Arveson and Kadison regarding a strong version of the Schur-Horn theorem in II₁ factors in terms of submajorization and contractive orbits of positive operators.