Quasisimilarity and compact perturbations
Abstract
In this paper we show that quasisimilar -tuples of tensor products of -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.
Cite
@article{arxiv.2510.09279,
title = {Quasisimilarity and compact perturbations},
author = {Salah Mecheri},
journal= {arXiv preprint arXiv:2510.09279},
year = {2025}
}