94-81 del Rio R., Makarov N., Simon B.
Operators with Singular Continuous Spectrum, II. Rank One Operators (23K, AMSTeX) Apr 5, 94
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Abstract. For an operator, $A$, with cyclic vector $\varphi$, we study $A+\lambda P$ where $P$ is the rank one projection onto multiples of $\varphi$. If $[\alpha,\beta] \subset \text{spec} (A)$ and $A$ has no a.c. spectrum, we prove that $A+\lambda P$ has purely singular continuous spectrum on $(\alpha,\beta)$ for a dense $G_\delta$ of $\lambda$\!'s.

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