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

Journal of Linear and Topological Algebra

مقاله 4، دوره 04، شماره 02، مرداد 2015، صفحه 131-142   

نوع مقاله: Research Paper

نویسندگان

F. Aboutorabi Goudarzi^* ؛ M. S. Asgari

Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran

چکیده

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 [16] to the situation of fusion basis.

کلیدواژه‌ها

Fusion Frame؛ Riesz fusion basis؛ Exact fusion frame؛ Orthonormal fusion basis

مراجع

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