As applications of Kadison's Pythagorean and carpenter's theorems, the Schur–Horn theorem, and Thompson's theorem, we obtain an extension of Thompson's theorem to compact operators and use these ideas to give a characterization of diagonals of …
Schur–Horn theorems focus on determining the diagonal sequences obtainable for an operator under all possible basis changes, formally described as the range of the canonical conditional expectation of its unitary orbit. Following a brief background …