Abstract
The similarity problem for restrictions of a non-selfadjoint operator with absolutely continuous spectrum to its spectral subspaces corresponding to arbitrary Borel subsets d of the spectrum is considered, generalizing the results of [7, 11]. Necessary and sufficient conditions of such similarity are obtained in the form of a pair of integral estimates on \(\delta \subset \mathbb{R}\). The results are then applied to the analysis of the one-dimensional non-selfadjoint Friedrichs model operator.
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