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Operators with singular continuous spectrum. II: Rank one operators. (English) Zbl 1055.47500
From the text: The main result is the following theorem: Let $$A$$ be selfadjoint with cyclic vector $$\phi$$ and corresponding rank-one projection $$P_\phi$$; then the set of $$\lambda$$ for which $$A_\lambda=A+\lambda P_\phi$$ has no eigenvalue in the spectrum of $$A$$ is a dense $$G_\delta$$ in $$\mathbb R$$. The authors also obtain a similar result for rank-one domain perturbations.
For Parts I and III–VII see Zbl 0851.47003, Zbl 0830.34074, Zbl 0908.47002, Zbl 0979.34063, Zbl 0846.47023, and Zbl 0848.34069.

##### MSC:
 47A10 Spectrum, resolvent 34L05 General spectral theory of ordinary differential operators 47A55 Perturbation theory of linear operators 47B25 Linear symmetric and selfadjoint operators (unbounded) 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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