Weighted Riesz bases in g-fusion frames and their perturbation

TL;DR

This paper explores the structure of g-fusion frames using weighted Riesz bases, establishing their fundamental properties, relationships with frames, and analyzing their stability under perturbations.

Contribution

It introduces orthonormal and Riesz bases for g-fusion frames, highlighting the importance of weights and providing new theorems and perturbation results.

Findings

Weights play a crucial role in g-fusion frames.

A key theorem links frames and g-fusion frames via operators.

Perturbation analysis shows stability of g-fusion frames.

Abstract

In this paper, we introduce orthonoramal and Riesz bases for g-fusion frames and will show that the weights have basic roles. Next, we prove an effective theorem between frames and g-fusion frames by using an operator. Finally, perturbations of g-fusion frames will be presented.