Variational principles and eigenvalue estimates for unbounded block operator matrices and applications
The authors consider three cases, the so-called ``top dominant'', the ``diagonal dominant'', and the ``off-diagonal dominant'' case depending on the position of the operators with smallest domain. In the case of differential operators, the dominating operators are those with the highest order. Examples for top dominant block operator matrices occur in magnetohydrodynamics or astrophysics, examples for the off-diagonal case appear in quantum mechanics (e.g., Dirac operators). They establish variational principles, eigenvalue estimates and asymptotic formulae for eigenvalues of these classes of unbounded block operator matrices. The results allow to characterise eigenvalues that are not necessarily located at the boundary spectrum. Applications to an example from magnetohydrodynamics and to Dirac operators on certain manifolds are given.
scientific article; zbMATH DE number 2085599