 9481 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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