Application of symmetric analytic functions to spectra of linear operators
Keywords: symmetric analytic function on a Banach space, $p$-nuclear operator, Fredholm determinant
Published online: 2021-12-11
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.
How to Cite
Burtnyak I., Chernega I., Hladkyi V., Labachuk O., Novosad Z. Application of Symmetric Analytic Functions to Spectra of Linear Operators. Carpathian Math. Publ. 2021, 13 (3), 701-710.