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

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.