English

Bessel sequences in Hilbert $C^{\ast}$-modules

Functional Analysis 2024-01-01 v1

Abstract

In this peaper we stady certain Bessel sequences {fk}k=1\left\{f_k\right\}_{k=1}^{\infty} in Hilbert C*- modules H\mathcal{H} for which operator SS defined by \ref{eq2} is of the form T+ξI\mathcal{T}+\xi I, for some real number ξ\xi and a adjointable linear operator T\mathcal{T}. Additionally, we investigate frames known as compact-tight frames, which have frame operators that are compact perturbations of constant multiples of the identity. As a conclusion, we provide a theory regarding the weaving of specific compact-tight frames.

Keywords

Cite

@article{arxiv.2312.17618,
  title  = {Bessel sequences in Hilbert $C^{\ast}$-modules},
  author = {Abdelilah Karara and Khadija Mabrouk},
  journal= {arXiv preprint arXiv:2312.17618},
  year   = {2024}
}