New Characterizations of Fusion Bases and Riesz Fusion Bases in Hilbert Spaces

摘要

In this paper we investigate a new notion of bases in Hilbert spaces andsimilar to fusion frame theory we introduce fusion bases theory in Hilbertspaces. We also introduce a new definition of fusion dual sequence associatedwith a fusion basis and show that the operators of a fusion dual sequence arecontinuous projections. Next we define the fusion biorthogonal sequence, Besselfusion basis, Hilbert fusion basis and obtain some characterizations of them.we study orthonormal fusion systems and Riesz fusion bases for Hilbert spaces.we consider the stability of fusion bases under small perturbations. We alsogeneralized a result of Paley-Wiener [13] to the situation of fusion basis.