Weighted eigenvalues of Dirac operators: complete continuity and comparison

We give a min-max characterization of the weighted Dirac eigenvalues, and show that the weighted eigenvalues and eigenspaces of Dirac operators are continuous with respect to weak $L^p$ convergence of the inverse weight, for any $p>n$. Moreover, we establish a comparison result for such weighted eigenvalue problems when there are no harmonic spinors.