Quasisimilarity and compact perturbations
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914086843842560 |
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| author | Mecheri, Salah |
| author_facet | Mecheri, Salah |
| contents | In this paper we show that quasisimilar $n$-tuples of tensor products of $m$-isometric operators have the same spectra, essential spectra and indices. The properties of single Fredholm operators possess \cite{4} is related to an important property which has a leading role on the theory of Fredholm operators: Fredholm n-tuples of operators. It is well known that a Fredholm operator of index zero can be perturbed by a compact operator to an invertible operator. In \cite[Problem 3]{5} the author asked if this property holds in several variables. R. Gelca in \cite{10} gave an example showing that this perturbation property fails in several variables. In this paper we give a positive answer to this question in case of tensor products of some classes of operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasisimilarity and compact perturbations Mecheri, Salah Functional Analysis In this paper we show that quasisimilar $n$-tuples of tensor products of $m$-isometric operators have the same spectra, essential spectra and indices. The properties of single Fredholm operators possess \cite{4} is related to an important property which has a leading role on the theory of Fredholm operators: Fredholm n-tuples of operators. It is well known that a Fredholm operator of index zero can be perturbed by a compact operator to an invertible operator. In \cite[Problem 3]{5} the author asked if this property holds in several variables. R. Gelca in \cite{10} gave an example showing that this perturbation property fails in several variables. In this paper we give a positive answer to this question in case of tensor products of some classes of operators. |
| title | Quasisimilarity and compact perturbations |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2510.09279 |