Robustness of controlled fusion frames under erasures of subspaces and the approximation operator

TL;DR

This paper investigates the stability of controlled fusion frames under subspace erasures, introduces an approximation operator for these frames, and examines the composition of such operators to enhance understanding of their robustness and applications.

Contribution

It presents new results on controlled fusion frames' behavior under erasures and introduces an approximation operator, expanding their theoretical framework and potential use cases.

Findings

Controlled fusion frames exhibit robustness under subspace erasures.

An approximation operator for controlled fusion frames is defined and analyzed.

The composition of operators from two controlled fusion frames is characterized.

Abstract

Controlled frames which presented to improve the numerical output of iterative algorithms for inverting the frame operator, have been introduced by Balazs and et al. Also, these frames are used by Bogdanova and et al. for spherical wavelets. In this note, we aim to study some new results about controlled fusion frames and behavior of them under erasures. Finally, we will introduce the approximation operator for these frames and a result of the composition of the operators of two controlled fusion frames will be proved.