new characterizations of fusion bases and riesz fusion bases in hilbert spaces

in this paper we investigate a new notion of bases in hilbert spaces and similarto fusion frame theory we introduce fusion bases theory in hilbert spaces. we also introducea new de nition of fusion dual sequence associated with a fusion basis and show that theoperators of a fusion dual sequence are continuous projections. next we de ne the fusionbiorthogonal sequence, bessel fusion basis, hilbert fusion basis and obtain some character-izations of them. we study orthonormal fusion systems and riesz fusion bases for hilbertspaces. we consider the stability of fusion bases under small perturbations. we also general-ized a result of paley-wiener [16] to the situation of fusion basis.