Advancements in the generalization of m-isometries: introducing the q-partial-(m, A)- isometry class
Abstract
In this paper, we extend the concepts ofm-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.