Abstract
In this paper several classes of self-adjoint and non-self-adjoint block operator matrices with unbounded entries are studied. The main results concern the existence of maximal spectral invariant subspaces which correspond to the right and the left half planes and their representation by means of angular operators. Sometimes this yields a diagonalization of the block operator matrix under consideration. Applications to abstract Dirac operators with supersymmetry and to Dirac operators with a potential are given.
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