Abstract:
We prove that if A is a self-adjoint operator and R a non-negative finite rank operator whose range is cyclic for A, then for a generic (in the Baire sense) t in $, each eigenvalue of the operator has a neighborhood containing no other eigenvalues.
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Received: 11 October 1996 / Accepted: 6 January 1997
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Gordon, A. Instability of Dense Point Spectrum Under Finite Rank Perturbations . Comm Math Phys 187, 583–595 (1997). https://doi.org/10.1007/s002200050150
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DOI: https://doi.org/10.1007/s002200050150