Given a self-adjoint, bounded-below, compactly-resolved operator $T$ densely defined in a Hilbert space, one method to study its eigenvalues is to consider the closure of its domain with respect to the norm $\langle Tu, u\rangle$.

However if $T$ is not positive, this is not a norm. So one considers instead the eigenvalues of operator $T + c$, where $c$ is chosen so that $T+c$ is positive. Apply the machinery to obtain eigenvalues of $T+c$.

Then the eigenvalues of $T$ are simply the eigenvalues of $T+c$, less $c$.