Application of symmetric analytic functions to spectra of linear operators
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 alge...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2021-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/5563 |
| _version_ | 1797205798090178560 |
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| author | I. Burtnyak I. Chernega V. Hladkyi O. Labachuk Z. Novosad |
| author_facet | I. Burtnyak I. Chernega V. Hladkyi O. Labachuk Z. Novosad |
| author_sort | I. Burtnyak |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T08:56:50Z |
| format | Article |
| id | doaj.art-97ee3ba4d42d48de80ee88b4a6ae7549 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:50Z |
| publishDate | 2021-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-97ee3ba4d42d48de80ee88b4a6ae75492024-04-16T07:09:07ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102021-12-0113370171010.15330/cmp.13.3.701-7104807Application of symmetric analytic functions to spectra of linear operatorsI. Burtnyak0https://orcid.org/0000-0002-9440-1467I. Chernega1V. Hladkyi2O. Labachuk3Z. Novosad4Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineInstitute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, UkraineVasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineVasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineLviv University of Trade and Economics, 10 Tuhan-Baranovskyi str., 79005, Lviv, UkraineThe 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.https://journals.pnu.edu.ua/index.php/cmp/article/view/5563symmetric analytic function on a banach space$p$-nuclear operatorfredholm determinant |
| spellingShingle | I. Burtnyak I. Chernega V. Hladkyi O. Labachuk Z. Novosad Application of symmetric analytic functions to spectra of linear operators Karpatsʹkì Matematičnì Publìkacìï symmetric analytic function on a banach space $p$-nuclear operator fredholm determinant |
| title | Application of symmetric analytic functions to spectra of linear operators |
| title_full | Application of symmetric analytic functions to spectra of linear operators |
| title_fullStr | Application of symmetric analytic functions to spectra of linear operators |
| title_full_unstemmed | Application of symmetric analytic functions to spectra of linear operators |
| title_short | Application of symmetric analytic functions to spectra of linear operators |
| title_sort | application of symmetric analytic functions to spectra of linear operators |
| topic | symmetric analytic function on a banach space $p$-nuclear operator fredholm determinant |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/5563 |
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