A Schur-Horn theorem in II$_1$ factors

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.

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