In this paper we establish variational principles, eigenvalue estimates and asymptotic formulae for eigenvalues of three different classes of unbounded block operator matrices. The results allow to characterise eigenvalues that are not necessarily located at the boundary of the spectrum. Applications to an example from magnetohydrodynamics and to Dirac operators on certain manifolds are given.
- variational principle for eigenvalues
- estimates for eigenvalues
- asymptotic distribution of eigenvalues
- quadratic numerical range
- warped product of spin manifolds
- dirac operator