Advancements in the generalization of m-isometries: introducing the q-partial-(m, A)-isometry class

Abstract

In this paper, we extend the concepts of m-partial isometry of order q and ( m , A ) -isometry, building on the contributions of Aouichaoui MA. [A note on partial-A-isometries and some applications. Quaest Math. 2024; 47(3):515–535], Bermúdez et al. [ ( m , A ) -isometries on Hilbert spaces. Linear Algebra Appl. 2018;540:95–111], Sadi A, Mahmoudi F. [ ( m , A ) -partial isometries in semi-Hilbertian spaces. Linear Multilinear Algebra. doi: 10.1080/03081087.2022.2068493], Sid Ahmed OAM, Saddi A. [A-m-Isometric operators in semi-Hilbertian spaces. Linear Algebra Appl. 2012;436(10):3930–3942], Sid Ahmed OAM. [Generalization of m-partial isometries on a Hilbert space. Int J Pure Appl Math. 2015;104(4):599–619]. Specifically, we introduce and define the class of q-partial- ( m , A ) -isometries, and provide a detailed analysis of their matrix representations. Additionally, we explore their spectral properties.