Non-commutative Schur-Horn theorems and extended majorization for Hermitian matrices

MASSEY, PEDRO

LINEAR AND MULTILINEAR ALGEBRA

TAYLOR & FRANCIS LTD

Lugar: Londres; Año: 2010 vol. 58 p. 465 - 480

0308-1087

Let \cA in Mn(C) be a unital *-subalgebra of the algebra Mn(C) of all nxn complexmatrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C)and let E_\cA denote the trace preserving conditional expectation onto \cA. We give a spectralcharacterization of the setE_\cA(Un(B)) = {E_\cA(U* B U) : U in Mn(C); unitary matrix }We obtain a similar result for the contractive orbit of a positive semi-denite matrix B. We thenuse these results to extend the notions of majorization and submajorization between self-adjointmatrices to spectral relations that come together with extended (non-commutative) Schur-Horntype theorems