Fusion frames for operators and atomic systems

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 and construct new K-fusion frames from given ones. We also study the stability of K-fusion frames under small perturbations. We further give some characterizations of atomic systems with subspace sequences.