@article{Burtnyak_Chernega_Hladkyi_Labachuk_Novosad_2021, title={Application of symmetric analytic functions to spectra of linear operators}, volume={13}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/5563}, DOI={10.15330/cmp.13.3.701-710}, abstractNote={<p>The paper is devoted to extension of the theory of symmetric analytic functions on Banach sequence spaces to the spaces of nuclear and $p$-nuclear operators on the Hilbert space. We introduced algebras of symmetric polynomials and analytic functions on spaces of $p$-nuclear operators, described algebraic bases of such algebras and found some connection with the Fredholm determinant of a nuclear operator. In addition, we considered cases of compact and bounded normal operators on the Hilbert space and discussed structures of symmetric polynomials on corresponding spaces.</p>}, number={3}, journal={Carpathian Mathematical Publications}, author={BurtnyakI. and ChernegaI. and HladkyiV. and LabachukO. and NovosadZ.}, year={2021}, month={Dec.}, pages={701-710} }