Application of symmetric analytic functions to spectra of linear operators

Authors

  • I. Burtnyak Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0002-9440-1467
  • I. Chernega Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
  • V. Hladkyi Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • O. Labachuk Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • Z. Novosad Lviv University of Trade and Economics, 10 Tuhan-Baranovskyi str., 79005, Lviv, Ukraine
https://doi.org/10.15330/cmp.13.3.701-710

Keywords:

symmetric analytic function on a Banach space, $p$-nuclear operator, Fredholm determinant
Published online: 2021-12-11

Abstract

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.

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How to Cite
(1)
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, 701-710.