(k,m, n)-partially isometric operators: A new generalization of partial isometries


Mohamed Amine Aouichaoui, Haïkel Skhiri




Asignificant amount of elegant work has been accomplished in the study of partial isometries. In this article, weintroduce a new class of operators, referred to as the (k,m, n)-partial isometries, which extends the concept of partial isometry. We delve into the most intriguing outcomes related to this class by extending previously established results for partial isometries and by exploring new results on partial isometries. We investigate the relationship of this new class of operators with classical notions of operators, such as partial isometries, power partial isometries, paranormal, semi-regular, and quasi-Fredholm. Additionally, we examine some fundamental properties and structure theorems of (k,m, n)-partial isometries. Furthermore, we provide spectral properties of (k,m, n)-partial isometries.