Abstract
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.
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