# Characterization of duals of continuous frames in Hilbert C*-modules

## TL;DR

This paper explores the properties and construction methods of dual continuous frames in Hilbert C*-modules, establishing a correspondence with adjointable operators and analyzing dual sum conditions.

## Contribution

It introduces a new characterization of duals, constructs dual families via fixed duals, and links duals to adjointable operators in Hilbert C*-modules.

## Key findings

- Established a one-to-one correspondence between duals and adjointable operators.
- Provided conditions for the sum of duals to also be a dual.
- Presented methods for constructing duals from a fixed dual.

## Abstract

In this paper, we investigate some characterizations of dual continuous frames and give some results about them. Also, we refer to the method of constructing a family of duals through a fixed dual and show there exists a one-to-one correspondence between duals of a continuous frame for Hilbert $C^*$-module $U$ and adjointable operators $K$ from $U$ to $L^{2}(\Omega ,\mathcal A)$. Then we check the conditions that the sum of two duals of a given continuous frame under the influence of adjointable mappings becomes a dual of it and state some results about them.