This is an announcement for the paper "New characterizations of fusion bases and Riesz fusion bases in hilbert spaces" by Mohammad Sadegh Asgari.

Abstract: In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new definition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we define the fusion biorthogonal sequence, Bessel fusion 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 also generalized a result of Paley-Wiener [13] to the situation of fusion basis.

Archive classification: math.FA

Mathematics Subject Classification: Primary 42C15, Secondary 46C99

Remarks: 14 pages

Submitted from: moh.asgari@iauctb.ac.ir

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1203.6279

or

http://arXiv.org/abs/1203.6279