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arXiv · 2106.14035

On the similarity of complex symmetric operators to perturbations of restrictions of normal operators

Sergey M. Zagorodnyuk
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Abstract

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.

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Sergey M. Zagorodnyuk. 2021-06-26. On the similarity of complex symmetric operators to perturbations of restrictions of normal operators. https://arxiv.org/abs/2106.14035

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