From https://arxiv.org/pdf/2101.12317 how is the simplification of equation (2.16) obtained?
Let $g(x),p(x)$ be real functions and $\lambda$ complex. Consider the expression $\langle g, (-\frac{d^2}{dx^2} + \lambda I)^{-1}g\rangle-\langle g, (-\frac{d^2}{dx^2} +(p+ \lambda I))^{-1}g\rangle$. I want to show this simplifies to, as stated in the paper, $$\langle (-\frac{d^2}{dx^2} + (p+\overline{\lambda})I)^{-1}g,p(\frac{d^2}{dx^2} + \lambda I)^{-1}g\rangle$$
However, I do not see how one applies the properties of an inner product to get this.