Application of symmetric analytic functions to spectra of linear operators - Burtnyak, I.; Chernega, I.; Hladkyi, V.; Labachuk, O.; Novosad, Z. (Carpathian Mathematical Publications, 2021)
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.