Some properties of Controlled Fusion Frames

TL;DR

This paper introduces new concepts and results on controlled fusion frames in Hilbert spaces, highlighting their advantages in numerical stability and robustness, along with the notion of Q-duality.

Contribution

It generalizes fusion frames by introducing controlled fusion frames and Q-duality, enhancing numerical stability and robustness in Hilbert space applications.

Findings

Controlled fusion frames improve numerical conditioning.

Introduction of Q-duality for controlled fusion frames.

Robustness of controlled fusion frames under perturbations.

Abstract

Controlled frames in Hilbert spaces have been introduced by Balazs, Antoine and Grybos to improve the numerical output of in relation to algorithms for inverting the frame operator. In this paper we have introduced and displayed some new concepts and results on controlled fusion frames for Hilbert spaces. It is shown that controlled fusion frames as a generalization of fusion frames give a generalized way to obtain numerical advantage in the sense of reconditioning to check the fusion frame condition. For this end, we introduce the notion of Q-duality for Controlled fusion frames. Also, we survey the robustness of Controlled fusion frames under some perturbations.