Abstract:
Let Mn be the C∗ algebra of n × n complex matrices and let ϕ : Mn → Mn be
a completely positive map. Suppose A ∈ Mn is a self-adoint matrix. We prove
a submajorization result concerning positive and negative parts of the spectrum
of ϕ(A). As a consequence, we obtain inequalities concerning the smallest and
the largest eigenvalues of the Schur product of A and B, where A and B are
self-adjoint.
