2 problems

Let $A$ be a self-adjoint operator with spectral components $[?]$ and $[?]$ separated by distance $d$, and let $V$ be a perturbation. Denote by $\mathsf{E}_A(\sigma)$ and…

Let ${\mathcal F}$, ${\mathcal G}$ and their perturbed counterparts be infinite-dimensional subspaces, and consider the sines and cosines of their angles. Unsquared angle-bound con…