New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces

Subject Areas : Functional analysis

F.  Aboutorabi Goudarzi ¹ (Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran)
M. S.  Asgari ² (Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran)

Received: 2015-06-20 Accepted : 2015-09-19 Published : 2015-05-01

Keywords: Fusion Frame, Riesz fusion basis, Exact fusion frame, Orthonormal fusion basis,

Abstract :

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 definition of fusion dual sequence associated with a fusion basis and show that theoperators of a fusion dual sequence are continuous projections. Next we define the fusionbiorthogonal sequence, Bessel fusion basis, Hilbert fusion basis and obtain some characterizations 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 generalized a result of Paley-Wiener [16] to the situation of fusion basis.

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