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 ...

We study refinements between spectral resolutions in an arbitrary II1 factor M and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. ...

Let A be an n×n complex Hermitian matrix and let λ(A)=(λ1,…,λn)∈Rn denote the eigenvalues of A, counting multiplicities and arranged in non-increasing order. Motivated by problems arising in the theory of low rank matrix ...

Let A be a C*-algebra and φ{symbol} : A → L (H) be a positive unital map. Then, for a convex function f : I → R defined on some open interval and a self-adjoint element a ∈ A whose spectrum lies in I, we obtain a Jensen's-type ...

In this paper we consider two problems in frame theory. On the one hand, given a set of vectors F we describe the spectral and geometrical structure of optimal completions of F by a finite family of vectors with prescribed ...

Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n×n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional ...