Invertibility of Generalized Bessel multipliers in Hilbert $C^{*}$-modules

TL;DR

This paper extends the theory of Bessel multipliers in Hilbert $C^*$-modules, providing conditions for their invertibility which is crucial for reconstruction in functional analysis.

Contribution

It introduces a generalized version of Bessel multipliers in Hilbert $C^*$-modules and thoroughly investigates the conditions for their invertibility.

Findings

Extended results for multipliers in Hilbert $C^*$-modules

Derived conditions for invertibility of generalized multipliers

Enhanced understanding of reconstruction formulas in this context

Abstract

In this note, a general version of Bessel multipliers in Hilbert $C^*$-modules is presented and then, many results obtained for multipliers are extended. Also the conditions for invertibility of generalized multipliers are investigated in details. The invertibility of multipliers is very important because it helps us to obtain more reconstruction formula.