Let $A,B\in\mathbb{C}^{p\times p}$ s.t. $A$ and $B$ are contractions and $I_p-AA^*$ and $BB^*$ both are positive semidefinite. I want to show that the matrix $$B(I_p-\sqrt{I_p-AA^*}\sqrt{I_p-AA^*}^*)B^*$$ is positive semidefinite. Are the conditions enough to show this? I'd much appreciate any help!
2026-03-24 23:43:19.1774395799
Is this matrix product positive semidefinite?
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