Open AccessApplication of symmetric analytic functions to spectra of linear operators
Author(s) -
Ivan Burtnyak,
Iryna Chernega,
V. Hladkyi,
O. V. Labachuk,
Zoriaovosad
Publication year - 2021
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.13.3.701-710
Subject(s) - mathematics , hilbert space , pure mathematics , compact operator on hilbert space , nuclear operator , bounded function , operator theory , analytic function , operator (biology) , unbounded operator , algebraic number , algebra over a field , finite rank operator , compact operator , banach space , extension (predicate logic) , mathematical analysis , biochemistry , chemistry , repressor , computer science , transcription factor , gene , programming language
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.