Abstract
In this paper we establish conditions for the existence of maximal J-semi-definite invariant subspaces of unbounded J-selfadjoint operators. Our results allow for operators where all entries of the formal matrix representation induced by the indefinite metric are unbounded and they do not require any definiteness or J-dissipativity assumptions. As a consequence of the existence of invariant subspaces, we obtain an unexpected result on the accumulation of non-real eigenvalues at the real axis which is of independent interest. An application to some dissipative two-channel Hamiltonians illustrates this new phenomenon.
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