# On Controlled Frames in Hilbert $C^*$-modules

## TL;DR

This paper introduces controlled frames in Hilbert C*-modules, explores their properties, characterizations, and related operators, and investigates their connections to weighted frames within this mathematical framework.

## Contribution

It extends the concept of controlled frames to Hilbert C*-modules, providing new characterizations and analyzing associated multiplier and weighted frames.

## Key findings

- Controlled frames share key properties with those in Hilbert spaces.
- Characterization of controlled frames in Hilbert C*-modules.
- Development of multiplier operators for controlled frames.

## Abstract

In this paper, we introduce controlled frames in Hilbert $C^*$-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. Next, we give a characterization of controlled frames in Hilbert $C^*$-module. Also multiplier operators for controlled frames in Hilbert $C^*$-modules will be defined and some of its properties will be shown. Finally, we investigate weighted frames in Hilbert $C^*$-modules and verify their relations to controlled frames and multiplier operators.