Spectral Fredholm Theory in Von Neumann Algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914715791261696 |
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| author | Ivkovic, Stefan |
| author_facet | Ivkovic, Stefan |
| contents | In this paper, we extend Fredholm theory in von Neumann algebras established by Breuer in [5] and [6] to spectral Fredholm theory. We consider 2 by 2 upper triangular operator matrices with coefficients in a von Neumann algebra and give the relationship between the generalized essential spectra in the sense of Breuer of such matrices and of their diagonal entries. Next, we prove that if a generalized Fredholm operator in the sense of Breuer has 0 as an isolated point of its spectrum, then the corresponding spectral projection is finite. Finally, we define the generalized B-Fredholm operator in a von Neumann algebra as a generalization in the sense of Breuer of the classical B-Fredholm operators on Hilbert and Banach spaces. We provide sufficient conditions under which a sum of a generalized B-Fredholm operator and a finite operator in a von Neumann algebra is again a generalized B-Fredholm operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral Fredholm Theory in Von Neumann Algebras Ivkovic, Stefan Operator Algebras In this paper, we extend Fredholm theory in von Neumann algebras established by Breuer in [5] and [6] to spectral Fredholm theory. We consider 2 by 2 upper triangular operator matrices with coefficients in a von Neumann algebra and give the relationship between the generalized essential spectra in the sense of Breuer of such matrices and of their diagonal entries. Next, we prove that if a generalized Fredholm operator in the sense of Breuer has 0 as an isolated point of its spectrum, then the corresponding spectral projection is finite. Finally, we define the generalized B-Fredholm operator in a von Neumann algebra as a generalization in the sense of Breuer of the classical B-Fredholm operators on Hilbert and Banach spaces. We provide sufficient conditions under which a sum of a generalized B-Fredholm operator and a finite operator in a von Neumann algebra is again a generalized B-Fredholm operator. |
| title | Spectral Fredholm Theory in Von Neumann Algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2403.10526 |