2025/10/10 by Salah Mecheri, Mecheri, Salah
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2510.09279
openalex publication_date 2025/10/10 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
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 \cite4 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 \cite10 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.