Fusion frames for operators and atomic systems

TL;DR

This paper introduces K-fusion frames, a generalization of fusion frames related to bounded operators, and explores their properties, stability, and atomic system characterizations in Hilbert spaces.

Contribution

It extends existing fusion frame theory to include K-fusion frames associated with bounded operators, providing new constructions and stability analysis.

Findings

New K-fusion frames constructed using bounded operators

Stability of K-fusion frames under small perturbations established

Characterizations of atomic systems with subspace sequences provided

Abstract

Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K which we call K-fusion frames. We obtain new K-fusion frames by considering K-fusion frames with a class of bounded linear operators. We also study the stability of K-fusion frames under small perturbations. We further give some characterizations of atomic systems with subspace sequences.