Normalized Orbit Frames and Essential Spectrum, II

James Tian

Given $0<r_j<1$ with $r_j\to 1$, there exist a normal operator $T$ on ${\ell }^2$ with eigenvalues ${\lambda }_j$ satisfying $|{\lambda }_j|=r_j$ and $g\in {\ell }^2$ such that \[ \left\{ \fra…