Application of symmetric analytic functions to spectra of linear operators

I. Burtnyak, I. Chernega, V. Hladkyi, O. Labachuk, Z. Novosad
2021 Karpatsʹkì Matematičnì Publìkacìï  
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
more » ... e and discussed structures of symmetric polynomials on corresponding spaces.
doi:10.15330/cmp.13.3.701-710 fatcat:viagxglzzvallgajzqqdo5qwbm