Spectra of frame operators with prescribed frame norms (Q2875846)

The authors obtain the probable set of finite spectra of frame operators with given frame norms. They define a \textit{spectral set} given by NEWLINE\[NEWLINE\begin{gathered} \mathcal{A}_n(\{d_i\}) = \{ (A_1, \dots , A_n) \in (0, 1)^n: \text{ for all } j \neq k, A_j \neq A_k, \\ \text{ there exists a self-adjoint operator } E \text{ on } \ell^2(I) \\ \text{ with } \sigma(E) = \{0,A_1, \dots ,A_n, 1\} \text{ and diagonal } \{d_i\}; n \in \mathbb{N}\}\end{gathered}NEWLINE\]NEWLINE and study its properties for \(n=1\) in the first subsection. The second subsection deals with the properties \(\mathcal{A}_n(\{d_i\})\) where n \(\geq 2\). The authors prove a result analogous to the Schur-Horn theorem in the later half. Examples for highlighting the results are also given.NEWLINENEWLINEFor the entire collection see [Zbl 1285.00036].