On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebras
Axiomatic Fredholm theory in unital C*-algebras was established in [D. Kečkić, Z. Lazović, Acta Sci. Math., 83(3-4):629--655, 2017]. Following the pure algebraic approach by Kečkić and Lazović, in the author's paper [S. Ivković, Banach J. Math. Anal., 17:51, 2023] we extended further this theor...
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2024-02-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
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| Online Access: | https://journals.ontu.edu.ua/index.php/geometry/article/view/2594 |
| _version_ | 1797303246618886144 |
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| author | Stefan Ivkovic |
| author_facet | Stefan Ivkovic |
| author_sort | Stefan Ivkovic |
| collection | DOAJ |
| description | Axiomatic Fredholm theory in unital C*-algebras was established in [D. Kečkić, Z. Lazović, Acta Sci. Math., 83(3-4):629--655, 2017]. Following the pure algebraic approach by Kečkić and Lazović, in the author's paper [S. Ivković, Banach J. Math. Anal., 17:51, 2023] we extended further this theory to axiomatic semi-Fredholm and semi-Weyl theory in unital C*-algebras. However, recently, in [S. Ivković, arXiv:2306.01133] we developed another approach to axiomatic Fredholm theory in unital C*-algebras which is based on the theory of Hilbert modules and is equivalent to the algebraic approach by Kečkić and Lazović. In this paper, we extend further that new Hilbert-module approach from Fredholm theory to semi-Fredholm and semi-Weyl theory in unital C*-algebras. Hence, we provide new proofs to the results in [S. Ivković, Banach J. Math. Anal., 17:51, 2023]. |
| first_indexed | 2024-03-07T23:50:07Z |
| format | Article |
| id | doaj.art-6e564b6fc3f444e0b83f5e26188cdc32 |
| institution | Directory Open Access Journal |
| issn | 2072-9812 2409-8906 |
| language | English |
| last_indexed | 2024-03-07T23:50:07Z |
| publishDate | 2024-02-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj.art-6e564b6fc3f444e0b83f5e26188cdc322024-02-19T08:47:40ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062024-02-0117111710.15673/pigc.v17i1.25942594On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebrasStefan Ivkovic0Mathematical Institute of the Serbian Academy of Sciences and ArtsAxiomatic Fredholm theory in unital C*-algebras was established in [D. Kečkić, Z. Lazović, Acta Sci. Math., 83(3-4):629--655, 2017]. Following the pure algebraic approach by Kečkić and Lazović, in the author's paper [S. Ivković, Banach J. Math. Anal., 17:51, 2023] we extended further this theory to axiomatic semi-Fredholm and semi-Weyl theory in unital C*-algebras. However, recently, in [S. Ivković, arXiv:2306.01133] we developed another approach to axiomatic Fredholm theory in unital C*-algebras which is based on the theory of Hilbert modules and is equivalent to the algebraic approach by Kečkić and Lazović. In this paper, we extend further that new Hilbert-module approach from Fredholm theory to semi-Fredholm and semi-Weyl theory in unital C*-algebras. Hence, we provide new proofs to the results in [S. Ivković, Banach J. Math. Anal., 17:51, 2023].https://journals.ontu.edu.ua/index.php/geometry/article/view/2594semi-fredholm operatorsemi-weyl operatorindexk-grouphilbert module |
| spellingShingle | Stefan Ivkovic On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebras Pracì Mìžnarodnogo Geometričnogo Centru semi-fredholm operator semi-weyl operator index k-group hilbert module |
| title | On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebras |
| title_full | On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebras |
| title_fullStr | On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebras |
| title_full_unstemmed | On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebras |
| title_short | On new approach to semi-Fredholm theory in unital C<sup>*</sup>-algebras |
| title_sort | on new approach to semi fredholm theory in unital c sup sup algebras |
| topic | semi-fredholm operator semi-weyl operator index k-group hilbert module |
| url | https://journals.ontu.edu.ua/index.php/geometry/article/view/2594 |
| work_keys_str_mv | AT stefanivkovic onnewapproachtosemifredholmtheoryinunitalcsupsupalgebras |