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arXiv · 2510.09279

Quasisimilarity and compact perturbations

Salah Mecheri
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Abstract

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.

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Salah Mecheri. 2025-10-10. Quasisimilarity and compact perturbations. https://arxiv.org/abs/2510.09279

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