# On continuous weaving fusion frames in Hilbert spaces

## TL;DR

This paper introduces the concept of weaving c-fusion frames in Hilbert spaces, providing conditions for their stability under operators, vector removal, and perturbations, advancing the theoretical understanding of frame structures.

## Contribution

It defines weaving c-fusion frames, establishes necessary and sufficient conditions for their properties, and explores their stability under various modifications.

## Key findings

- Conditions for maintaining weaving c-fusion frames under bounded operators
- Criteria for removing vectors while preserving frame properties
- Perturbation results ensuring frame stability

## Abstract

In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors from these frames, we will present a necessarily and sufficient condition about c-woven and c-fusion woven. Finally, perturbation of these frames will be introduced.