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

Abstract

In this peaper we stady certain Bessel sequences ${\left\{f_k\right\}}_{k=1}^{\infty }$ in Hilbert C*- modules $\mathcal{H}$ for which operator $S$ defined by \ref{eq2} is of the form $\mathcal{T}+\xi I$, for some real number $\xi$ and a adjointable linear operator $\mathcal{T}$. 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.