Sergey M. Zagorodnyuk
Published 2021-06-26Version 1
In this paper we consider a problem of the similarity of complex symmetric operators to perturbations of restrictions of normal operators. For a subclass of cyclic complex symmetric operators in a finite-dimensional Hilbert space we prove the similarity to rank-one perturbations of restrictions of normal operators. The main tools are a truncated moment problem in $\mathbb{C}$, and some objects similar to objects from the theory of spectral problems for Jacobi matrices.
On the metric of the jet bundle and similarity on Dirichlet spaces
On $n$th roots of normal operators
New Reverse Inequalities for the Numerical Radius of Normal Operators in Hilbert Spaces
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