The author studies the spectrum of dissipative Schrödinger operators. It is known that the eigenvalues of the Schrödinger operator − ∆ + V1 with decaying realvalued potential V1 cannot accumulate to 0. The author proves that such a property still appears in dimension larger than 3 for dissipative perturbation, i.e., for the complex-valued potential V = V1 + iV2 whose the real and imaginary parts are decaying and the imaginary part V2 is non-positive (and negative on some nontrivial open set). Then the author studies the number of eigenvalues of the Schrödinger operator − ∆ + V1 + iV2 when the imaginary part V2 of the potential is small enough and links this number with the number of eigenvalues of the Schrödinger operator − ∆ + V1
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