Open AccessPerturbation of the spectra of complex symmetric operators
Author(s) -
Qinggang Bu,
Cun Wang
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2101191b
Subject(s) - mathematics , orthonormal basis , hilbert space , perturbation (astronomy) , pure mathematics , complex space , symmetric space , separable space , operator (biology) , mathematical analysis , quantum mechanics , physics , biochemistry , chemistry , repressor , transcription factor , affine transformation , gene
An operator T on a complex Hilbert space H is called complex symmetric if T has a symmetric matrix representation relative to some orthonormal basis for H. This paper focuses on the perturbation theory for the spectra of complex symmetric operators. We prove that each complex symmetric operator on a complex separable Hilbert space has a small compact perturbation being complex symmetric and having the single-valued extension property. Also it is proved that each complex symmetric operator on a complex separable Hilbert space has a small compact perturbation being complex symmetric and satisfying generalized Weyl?s theorem.