Thompson's theorem for compact operators and diagonals of unitary   operators
  As applications of Kadison's Pythageorean and carpenter's theorems, the Schur-Horn theorem, and Thompson's theorem, we obtain an extension of Thompsons theorem to compact operators and use these ideas to give a characterization of diagonals of unitary operators. Thompson's mysterious inequality concerning the last terms of the diagonal and singular value sequences plays a central role. 
John Jasper and Jireh Loreaux and Gary Weiss
math.FA