## Determinant of quotient of unbounded operators

I have been trying to prove this for a while but failed so far. Let $A$ and $B$ are two positive, self-adjoint operators with compact resolvent on a Hilbert space $H$ defined on the same dense domain $D \subset H$ and suppose that $A^{-1}B$ extends from $D$ to a bounded operator on all of $H$. … Read more