{ "id": "2106.14035", "version": "v1", "published": "2021-06-26T14:42:15.000Z", "updated": "2021-06-26T14:42:15.000Z", "title": "On the similarity of complex symmetric operators to perturbations of restrictions of normal operators", "authors": [ "Sergey M. Zagorodnyuk" ], "comment": "13 pages", "categories": [ "math.FA" ], "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.", "revisions": [ { "version": "v1", "updated": "2021-06-26T14:42:15.000Z" } ], "analyses": { "subjects": [ "47A20" ], "keywords": [ "normal operators", "similarity", "restrictions", "cyclic complex symmetric operators", "finite-dimensional hilbert space" ], "note": { "typesetting": "TeX", "pages": 13, "language": "en", "license": "arXiv", "status": "editable" } } }