Finite-rank perturbations of positive operators and isometries
Man-Duen Choi, Pei Yuan Wu · Studia Mathematica · 2006
We completely characterize the ranks of $A-B$ and $A^{1/2}-B^{1/2}$ for operators $A$ and $B$ on a Hilbert space satisfying $A\geq B\geq 0$. Namely, let $l$ and $m$ be nonnegative integers or infinity. Then $l=\mathop{\rm rank} (A-B)$ and $m=\mathop{\rm r