Point spectrum and mixed spectral types for rank one perturbations
Point spectrum and mixed spectral types for rank one perturbations
We consider examples $A_{\lambda }= A+\lambda (\varphi , \cdot )\varphi$ of rank one perturbations with $\varphi$ a cyclic vector for $A$. We prove that for any bounded measurable set $B\subset I$, an interval, there exist $A, \varphi$ so that $\{ E\in I \mid {}$ some $A_\lambda$ has $E$ as an …