Abstract
In this paper we investigate the connection between fusion frames and obtain a relation between indexes of the synthesis operators of a Besselian fusion frame and associated frame to it. Next we introduce a new notion of a Riesz fusion bases in a Hilbert space. We show that any Riesz fusion basis is equivalent with a orthonormal fusion basis. We also obtain generalizations of Theorem 4.6 of [1]. Our results generalize results obtained for Riesz bases in Hilbert spaces. Finally we obtain some results about stability of fusion frame sequences under small perturbations
Contents
1. Introduction
2. Characterization of fusion frames by frames
3. Fusion bases and Riesz fusion bases
4. Stability of fusion frame sequences under perturbations