Abstract
We show that various Hamiltonians and Jacobi matrices have no absolutely continuous spectrum by showing that under a trace class perturbation they become a direct sum of finite matrices.
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Communicated by A. Jaffe
Dedicated to Roland Dobrushin
Research partially funded under NSF grant number DMS-8801918
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Simon, B., Spencer, T. Trace class perturbations and the absence of absolutely continuous spectra. Commun.Math. Phys. 125, 113–125 (1989). https://doi.org/10.1007/BF01217772
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DOI: https://doi.org/10.1007/BF01217772